Can someone help me to find suttas on Self compassion

This isn't quite what you were asking, but on the subject of "too much guilt instead of improving ourselves", there's SN 42.8 which includes --

Take some teacher who has this doctrine and view: ‘Everyone who kills a living creature, steals, commits sexual misconduct, or lies goes to a place of loss, to hell.’ And there’s a disciple who is devoted to that teacher. They think: ‘My teacher has this doctrine and view: ‘Everyone who kills a living creature, steals, commits sexual misconduct, or lies goes to a place of loss, to hell.’ But I’ve killed living creatures … stolen … committed sexual misconduct … or lied. They get the view: ‘I too am going to a place of loss, to hell.’ Unless they give up that speech and thought, and let go of that view, they will be cast down to hell.

But consider when a Realized One arises in the world, perfected, a fully awakened Buddha, accomplished in knowledge and conduct, holy, knower of the world, supreme guide for those who wish to train, teacher of gods and humans, awakened, blessed. In many ways he criticizes and denounces killing living creatures, saying: ‘Stop killing living creatures!’ He criticizes and denounces stealing … sexual misconduct … lying, saying: ‘Stop lying!’ And there’s a disciple who is devoted to that teacher. Then they reflect: ‘In many ways the Buddha criticizes and denounces killing living creatures, saying: “Stop killing living creatures!” But I have killed living creatures to a certain extent. That’s not right, it’s not good, and I feel remorseful because of it. But I can’t undo what I have done.’ Reflecting like this, they give up killing living creatures, and in future they don’t kill living creatures. That’s how to give up this bad deed and get past it.

Some other points:

• My first impression of "compassion" is that it's other-directed, directed toward others, and so "self-compassion" is a bit of a contradiction in terms -- for example,

  The world suffers. But most men have their eyes and ears closed. They do not see the unbroken stream of tears flowing through life; they do not hear the cry of distress continually pervading the world. Their own little grief or joy bars their sight, deafens their ears. Bound by selfishness, their hearts turn stiff and narrow. Being stiff and narrow, how should they be able to strive for any higher goal, to realize that only release from selfish craving will effect their own freedom from suffering?

  It is compassion that removes the heavy bar, opens the door to freedom, makes the narrow heart as wide as the world. Compassion takes away from the heart the inert weight, the paralyzing heaviness; it gives wings to those who cling to the lowlands of self.

  Through compassion the fact of suffering remains vividly present to our mind, even at times when we personally are free from it. It gives us the rich experience of suffering, thus strengthening us to meet it prepared, when it does befall us.

  Compassion reconciles us to our own destiny by showing us the life of others, often much harder than ours.

• Nevertheless the practice of Metta Bhavana -- as derived from the Metta Gatha -- starts with,

  May I be free from enmity and danger

  ... before going on to wish the same for everyone else.

  See also No compassion, goodwill for oneself?

• Also, while I'm on subject of the "self-or-others", I remember the Dalai Lama saying that he sees himself as being "just like everyone else, no different".

• I don't think that that the suttas say much about compassion, specifically -- normally it's mentioned in the context of being one of the four brahmaviharas.

  One place it's mentioned is MN 26, as the reason for the Buddha's consenting to teach:

  Then, understanding Brahmā’s invitation, I surveyed the world with the eye of a Buddha, because of my compassion for sentient beings.

  Another is AN 6.13 where it's antithetical to harming:

  Take another mendicant who says: ‘I’ve developed the heart’s release by compassion. I’ve cultivated it, made it my vehicle and my basis, kept it up, consolidated it, and properly implemented it. Yet somehow the thought of harming still occupies my mind.’ They should be told, ‘Not so, venerable! … For it is the heart’s release by compassion that is the escape from thoughts of harming.

There are a couple of suttas mentioned as Basic Wisdom:

• This is the way leading to discernment: when visiting a brahman or contemplative, to ask: 'What is skillful, venerable sir? What is unskillful? What is blameworthy? What is blameless? What should be cultivated? What should not be cultivated? What, when I do it, will be for my long-term harm & suffering? Or what, when I do it, will be for my long-term welfare & happiness?'"

  MN 135

• Whenever you want to perform a [bodily, verbal, and/or mental] act, you should reflect on it: 'This [...] act I want to perform — would it lead to self-affliction, to the affliction of others, or to both? Is it an unskillful [...] act, with painful consequences, painful results?' If, on reflection, you know that it would lead to self-affliction, to the affliction of others, or to both; it would be an unskillful [...] act with painful consequences, painful results, then any [...] act of that sort is absolutely unfit for you to do. But if on reflection you know that it would not cause affliction... it would be a skillful [...] action with happy consequences, happy results, then any [...] act of that sort is fit for you to do.

  MN 61

If "wanting to not cause harm" is an essential component of compassion, these suttas seems to support your thesis, i.e. that compassion should be developed "in all directions", "inwards and outwards", towards "self and others".

Incidentally, though this may be too fine a distinction to try and teach someone, I don't think this is the same as saying "self is good" or "self should be cherished" -- it's not speaking in praise of self-view, instead it's speaking against harm and oppression ...

ahita
harm; unkindliness. (adj.) harmful.

vyābādha & byābādha
oppression, injury, harm, hurting; usually in phrase atta˚ & para˚; (disturbing the peace of others of oneself) MN.i.89; SN.iv.339; AN.i.114, AN.i.157, AN.i.216; AN.ii.179-Also at SN.iv.159

... which is true both of "self-harm" and of "others'-harm".

I can recall these lines;

Seeing others as yourself; don't wish suffering on anyone. One protects others by protecting oneself; one protects oneself by protecting others.

You may be interested in AN 3.99, which states that by developing yourself in body, virtue and mind, a trifling evil deed that is done, will not bog you down:

"Suppose that a man were to drop a salt crystal into a small amount of water in a cup. What do you think? Would the water in the cup become salty because of the salt crystal, and unfit to drink?"

"Yes, lord. Why is that? There being only a small amount of water in the cup, it would become salty because of the salt crystal, and unfit to drink."

"Now suppose that a man were to drop a salt crystal into the River Ganges. What do you think? Would the water in the River Ganges become salty because of the salt crystal, and unfit to drink?"

"No, lord. Why is that? There being a great mass of water in the River Ganges, it would not become salty because of the salt crystal or unfit to drink."

"In the same way, there is the case where a trifling evil deed done by one individual [the first] takes him to hell; and there is the case where the very same sort of trifling deed done by the other individual is experienced in the here & now, and for the most part barely appears for a moment.

'Now, a trifling evil act done by what sort of individual takes him to hell? There is the case where a certain individual is undeveloped in the body, undeveloped in virtue, undeveloped in mind [i.e., painful feelings can invade the mind and stay there], undeveloped in discernment: restricted, small-hearted, dwelling with suffering. A trifling evil act done by this sort of individual takes him to hell.

'Now, a trifling evil act done by what sort of individual is experienced in the here & now, and for the most part barely appears for a moment? There is the case where a certain individual is developed in the body, developed in virtue, developed in mind [i.e., painful feelings cannot invade the mind and stay there], developed in discernment: unrestricted, large-hearted, dwelling with the immeasurable. A trifling evil act done by this sort of individual is experienced in the here & now, and for the most part barely appears for a moment.

From SN 42.8, we get a similar message:

"There's the case, headman, where a certain teacher holds this doctrine, holds this view: 'All those who take life are destined for a state of deprivation, are destined for hell. All those who steal... All those who indulge in illicit sex... All those who tell lies are destined for a state of deprivation, are destined for hell.' A disciple has faith in that teacher, and the thought occurs to him, 'Our teacher holds this doctrine, holds this view: "All those who take life are destined for a state of deprivation, are destined for hell." There are living beings that I have killed. I, too, am destined for a state of deprivation, am destined for hell.' He fastens onto that view. If he doesn't abandon that doctrine, doesn't abandon that state of mind, doesn't relinquish that view, then as if he were to be carried off, he would thus be placed in hell.

"[The thought occurs to him,] 'Our teacher holds this doctrine, holds this view: 'All those who steal... All those who indulge in illicit sex... All those who tell lies are destined for a state of deprivation, are destined for hell.' There are lies that I have told. I, too, am destined for a state of deprivation, am destined for hell.' He fastens onto that view. If he doesn't abandon that doctrine, doesn't abandon that state of mind, doesn't relinquish that view, then as if he were to be carried off, he would thus be placed in hell.

"There is the case, headman, where a Tathagata appears in the world, worthy and rightly self-awakened, consummate in clear knowing & conduct, well-gone, a knower of the cosmos, unexcelled trainer of those to be tamed, teacher of human & divine beings, awakened, blessed. He, in various ways, criticizes & censures the taking of life, and says, 'Abstain from taking life.' He criticizes & censures stealing, and says, 'Abstain from stealing.' He criticizes & censures indulging in illicit sex, and says, 'Abstain from indulging in illicit sex.' He criticizes & censures the telling of lies, and says, 'Abstain from the telling of lies.'

"A disciple has faith in that teacher and reflects: 'The Blessed One in a variety of ways criticizes & censures the taking of life, and says, "Abstain from taking life." There are living beings that I have killed, to a greater or lesser extent. That was not right. That was not good. But if I become remorseful for that reason, that evil deed of mine will not be undone.' So, reflecting thus, he abandons right then the taking of life, and in the future refrains from taking life. This is how there comes to be the abandoning of that evil deed. This is how there comes to be the transcending of that evil deed.

"[He reflects:] 'The Blessed One in a variety of ways criticizes & censures stealing... indulging in illicit sex... the telling of lies, and says, "Abstain from the telling of lies." There are lies that I have told, to a greater or lesser extent. That was not right. That was not good. But if I become remorseful for that reason, that evil deed of mine will not be undone.' So, reflecting thus, he abandons right then the telling of lies, and in the future refrains from telling lies. This is how there comes to be the abandoning of that evil deed. This is how there comes to be the transcending of that evil deed.

"Having abandoned the taking of life, he refrains from taking life. Having abandoned stealing, he refrains from stealing. Having abandoned illicit sex, he refrains from illicit sex. Having abandoned lies, he refrains from lies. Having abandoned divisive speech, he refrains from divisive speech. Having abandoned harsh speech, he refrains from harsh speech. Having abandoned idle chatter, he refrains from idle chatter. Having abandoned covetousness, he becomes uncovetous. Having abandoned ill will & anger, he becomes one with a mind of no ill will. Having abandoned wrong views, he becomes one who has right views.

"That disciple of the noble ones, headman — thus devoid of covetousness, devoid of ill will, unbewildered, alert, mindful — keeps pervading the first direction [the east] with an awareness imbued with good will, likewise the second, likewise the third, likewise the fourth. Thus above, below, & all around, everywhere, in its entirety, he keeps pervading the all-encompassing cosmos with an awareness imbued with good will — abundant, expansive, immeasurable, without hostility, without ill will. Just as a strong conch-trumpet blower can notify the four directions without any difficulty, in the same way, when the awareness-release through good will is thus developed, thus pursued, any deed done to a limited extent no longer remains there, no longer stays there.

"That disciple of the noble ones — thus devoid of covetousness, devoid of ill will, unbewildered, alert, mindful — keeps pervading the first direction with an awareness imbued with compassion... appreciation... equanimity, likewise the second, likewise the third, likewise the fourth. Thus above, below, & all around, everywhere, in its entirety, he keeps pervading the all-encompassing cosmos with an awareness imbued with equanimity — abundant, expansive, immeasurable, without hostility, without ill will. Just as a strong conch-trumpet blower can notify the four directions without any difficulty, in the same way, when the awareness-release through equanimity is thus developed, thus pursued, any deed done to a limited extent no longer remains there, no longer stays there."