The way I looked on it (eventually) was that the responsibility I had to my children (not grown up at the time of divorce, and I'll be another to say that more than 1 child does not always make for best friends...) was to model being strong and independent for them. That was my incentive to do things that were hard for me (and especially felt I didn't deserve, an issue mostly rectified with counselling), such as:
self-care - not always wearing jeans, painting toenails, wearing a necklace
social life - reaching out to friends, saying yes to invitations, trying new things
activity levels - getting out of the house most days, writing lists of 3 things to get done each day
And equally, if you are having a terrible day, do not beat yourself up if the most you can do is watch tv in bed eating toast. You need to heal.
Now that they are adults, they also wish they had had a better childhood and parents that got on, but they completely understand and accept that it could not be. And now even more than ever I feel thst my job as their role model is to show them that this little life that we have is not a burden to be endured, despite its many tricky parts, rather a path dotted about with many small joys.
We can all see that you are being far too hard on yourself, and I think you know it really but are finding it hard to stop blaming yourself and feeling regretful. If you feel it is to a point that you are finding it hard to function, maybe talk to the doctor again and a mild anti-depressant like cetirizine could be useful for a few months.