Can I save my meditation practice or should I abandon it?

Meditation, if done properly, is the super skill that amplifies every mental and physical skill you do in life. It would be stupid to stop meditation. The only question is whether you're doing meditation properly, skillfully, correctly, etc. You've got a great daily habit established, 20min in morning and one in latter half of the day, and regularly small meditation sessions all through the day.

Clearly the insomnia is the problem you need to take care of. If you don't have adequate nutrition and physical health, then meditation is less likely to have obvious immediate benefits.

Whatever you need to do to fix your health problems, take care of that first, and maybe with your time constraints you might have to suspend meditation temporarily.

In general you can stop what you are doing if you think it's causing you anxiety.

Although im not familiar with headspace, meditation usually fails as being ineffective rather than harmful. There are however ways in which one's training would cause anxiety & restlessness but i think it's unlikely here because i think it would be more obvious.

Imho, more likely than not & based on the info in op, you seem to have many duties and the meditation is not improving the quality of your life which probably makes you anxious about the training, questioning whether it's worth it.

Id try to drop it until you feel like doing it again or learn more so that it becomes worthwhile.

"Suppose that there is a foolish, inexperienced, unskillful cook who has presented a king or a king's minister with various kinds of curry: mainly sour, mainly bitter, mainly peppery, mainly sweet, alkaline or non-alkaline, salty or non-salty. He does not take note of[1] his master, thinking, 'Today my master likes this curry, or he reaches out for that curry, or he takes a lot of this curry, or he praises that curry. Today my master likes mainly sour curry... Today my master likes mainly bitter curry... mainly peppery curry... mainly sweet curry... alkaline curry... non-alkaline curry... salty curry... Today my master likes non-salty curry, or he reaches out for non-salty curry, or he takes a lot of non-salty curry, or he praises non-salty curry.' As a result, he is not rewarded with clothing or wages or gifts. Why is that? Because the foolish, inexperienced, unskillful cook does not pick up on the theme of his own master.

"In the same way, there are cases where a foolish, inexperienced, unskillful monk remains focused on the body in & of itself — ardent, alert, & mindful — putting aside greed & distress with reference to the world. As he remains thus focused on the body in & of itself, his mind does not become concentrated, his defilements[2] are not abandoned. He does not take note of that fact.[3] He remains focused on feelings in & of themselves... the mind in & of itself... mental qualities in & of themselves — ardent, alert, & mindful — putting aside greed & distress with reference to the world. As he remains thus focused on mental qualities in & of themselves, his mind does not become concentrated, his defilements are not abandoned. He does not take note of that fact. As a result, he is not rewarded with a pleasant abiding here & now, nor with mindfulness & alertness. Why is that? Because the foolish, inexperienced, unskillful monk does not take note of his own mind.[4] https://www.accesstoinsight.org/tipitaka/sn/sn47/sn47.008.than.html

There is a time for practice and there is a time for learning.

I'm no expert, but I've been meditating consistently for several years & have been on retreat etc. so I have some experience of what you have gone through. I strongly recommend finding a meditation teacher. Its hard to tell what's going on based on an internet post because there are so many factors; when you 'meditate', what are you actually doing, what are you doing in your day to day life, how is your sila (morality), are you on any medication etc. An experienced teacher will be able to pinpoint things in your practice you might not have been aware of and will be much more helpful than any advice you can get from internet strangers.

However, I now find myself really frustrated because I've actually started to get more anxious, and I've barely slept for the past month.

If this is a big issue for you, I think you should cease your practice for a while, at least just to see if it gets better. Its hard to tell without knowing more information, but it could be caused by you meditating 'wrongly'; i.e. following the anxious thought train & reinforcing the thought loops/ having wrong sila, or it could just be how your mind was all along, just that meditation made you aware of it. Only a teacher can guide you on this. All the best

Welcome to the site.

These anxieties are your own psychological issues. They bubble up to the surface as a result of meditation.

Meditation initially sounds all nice and pleasant with frilly bits and squishy things - although that is how it is generally delivered in the many brochures - but many don't realize what meditation can actually do. It is about the cold, hard reality of facing yourself, and sometimes what we see is gruesome and disturbing. It can be very uncomfortable, but once all that stuff is out, it leads to a great liberation.

Just be aware that if you decide to continue, it may have ramifications upon your life and family. Some people are just not ready to enter into that part of their psyche. That's for you to work out.