What can I do regarding Non-Self

The scriptures (AN 3.38) report, before his enlightenment to Buddhahood, when the unenlightened Gotama lived in three palaces, he had the vision he would get old, sick & die and this vision made him lose intoxication with his youth & life.

Then upon enlightenment, he fully realised the five aggregates that compose life (body, feelings, perception, thought function & sense consciousness) are 'not-self'; and one reason why each of the five aggregates cannot be a 'self' is because each can be subject to affliction & sickness that cannot be controlled (refer to beginning of SN 22.59).

It is reported the Buddha once taught to an elderly man that:

The body is afflicted, weak & encumbered. For who, looking after this body, would claim even a moment of true health, except through sheer foolishness?

SN 22.1

Therefore, although Gotama's original vision of death as a youth resulted in great angst in his mind & a long experimental spiritual search, in the end, his Buddhahood was merely the full acceptance & thus being at complete peace with his original vision of inevitable decay, death & impermanence.

In your situation, the place to go is the development of meditative calm (samatha) & clear insight (vipassana) so the mind is at complete peace & freedom with illness, aging & death (rather than having discomfort with this initial vision). In Buddhism, this is called reaching the 'Deathless'.

Monks, mindfulness of death — when developed & pursued — is of great fruit & great benefit. It gains a footing in the Deathless, has the Deathless as its final end (culmination).

AN 6.20

In seeing a glimpse of one insight into Dhamma (a rather big part of the Path at that) – that life is Not-Self – you now wonder what next. Now it is good to go deeper into Buddha’s teachings on inconstancy (Anitya), stress (Dukkha), and not self (Anatma). For this understanding and insight into Samma Dhitti to truly sink into you will take time. It is a given. The heart of the Noble Eightfold Path is Right Concentration. The other seven factors of the path are pre-requisites to come to that.

If you could take all three characteristics, that anything and everything in life is inconstant, stressful, and not self, and focus on them properly, it will have a big impact. Then you will be clearly established in the road to put an end to suffering. So now is the time for you to will into being the first seven qualities of the Noble Eightfold Path. Desire is a very important factor of the path towards this. Your desire to work towards this goal should far exceed all of your other worldly desires. Only then will you be able to focus on this properly, and to create the right conditions for it. Then you will start developing skilful qualities in your mind. So the first thing that you should do is to associate with people who will encourage you in this direction. Finding the right people to associate goes a long way in furthering in this Dhamma Path. This one factor will help instil an unflinching faith in the Buddha’s awakening. This is paramount. Instilling of ‘Saddha’ is more important than anything else, as it will carry you through the rest of the way.

You wrote, "things are just out of our control".

If seeing things as impermanent and non-self is Right View, the next factors on the Eightfold Path are Right Resolve, the training in virtue (Right Speech, Action, and Livelihood), and Right Effort and so on.

The fact that there is Right Resolve, Right Effort and so implies that things aren't out of our control, or at least, not all things: for example we can (at least to some extent) control resolve, speech, effort.

Doctrine about karma suggests we can also control intention, or that we're responsible for our intentional acts.

One of the suttas (Ittha Sutta: What is Welcome (AN 5.43)) says,

Now, I tell you, these five things are not to be obtained by reason of prayers or wishes. If they were to be obtained by reason of prayers or wishes, who here would lack them? It's not fitting for the disciple of the noble ones who desires long life to pray for it or to delight in doing so. Instead, the disciple of the noble ones who desires long life should follow the path of practice leading to long life. In so doing, he will attain long life, either human or divine.

The wise person, heedful,
acquires a two-fold welfare:
welfare in this life &
welfare in the next.
By breaking through to his welfare
he's called prudent,
wise.

You said, "when we are on the plane for example and there's turbulence and it's all in the hands of the elements, physics and fate."

That's true to a certain extent. It's also in the hands of the pilot; of the people who designed, tested, and certified the plane; and in your hands when you chose whether and how to travel.

So I see the anatta view as a helpful when you can't control (e.g. after you're on the plane); but you can (try to) control whether you make a good (prudent) decision before you get on the plane. Making a good (virtuous) decision can result in a "lack of remorse" (I don't mind being on a plane ... it was the right decision to make, at the time when I made that decision).

Seeing everything as uncontrollable and inevitably dying may be an extreme (an extreme which Buddhism calls, in English, "nihilism" or "annihilationism", and is considered one of the "wrong views").

I think the definition of "Non-self" is that it's better not to think too much about the self, nor to have definite views about the self. There are other things (apart from Self) that it's good to consider: other people, Dhamma, Sila, and so on. And the classic formulation of Non-Self isn't "this is out of my control", it's "this isn't me and this isn't mine", precisely because having views of self like "this is my body (and it's out of my control)" lead to suffering.

"Is there anywhere to go from here?" You go where your desires take you until you are ready to accept right where you are but we all push away where we are and cling to something else. We all do so, in some way or another unless we have mastered the Buddha'Eightfold Path(or a similar path).

Be nonreactive and impartial with things as they are as they occur and you will see how you can have peace and happiness. How? Follow the Buddha's Eightfold Path.