Hiya, I can relate. In the last year we moved countries, homes, and schools, with a 12 and 14 year old.
I totally agree with the lists. I tend to break it done into what I want to do weekly, in day form. And at the moment, given the way you are feeling, please be very conservative in what you ask/demand of yourself. Some days, it may be an achievement to get out of bed, not kill anybody, get food down everybody and then go back to bed.
With reference to wanting to feel better physically, what I found, was that when I forced myself to get outside, every day, and go for a walk, things felt a lot better. Particularly if the sun is shining. I'm taking vitamin D, and vitamin B, plus magnesium and a pro-biotic, which has helped me feel a lot better. With the nausea, I just accepted that sometimes I could eat, sometimes I could not, and that took the pressure off. Smoothies help make sure you get something down you.
With your 13 year old - well, they've got a right to feel how they do, regardless of how good our reasons are, their world has been turned upside down, and without their say so! I found accepting and sympathising with how they felt helped a great deal - however, that was not allowed to be expressed in rudeness, anger and hostility at me. Ask them if they need to see someone to talk to about it. Mine found art and journalling helped. If there is any room in the budget for a touch of bribery, that can help. Also, just doing things that show you care helps, cooking their favourite meal, encouraging new friendships, that sort of thing.
Sorry for the novel. I hope you feel better soon.