I have a chronic illness and I have three children, although I expect they are older than yours. The nature of my illness is that I can be absolutely fine for long stretches but on my arse for a month, now and again. I think I was out of action longest when I had, and was recovering from pneumonia, which spanned the entirety of the six week holidays and that was miserable.
Firstly, you need to give yourself a bit of leeway to be imperfect. Screen time might not be ideal but it is useful, identify when is the hardest part of your day and then employ it when it helps you the most.
Now you need to think about ways that you can help them exert energy while you do not. This is why I asked how old they are, this will be hardest with the smallest of children. So this could be finding a park where they are more easily contained and you can sit down. Or a soft play area. Or a place that you can oversee an activity like bowling or swimming from the sidelines. Basically you are looking to create a massive energy gap between you and your kids.
Logistically, with food and housework, consider yourself on a war footing. Paper plates and bowls to bin. Prepared food in the freezer to nuke. Spend money on convenience when/ if you can, cook meals are good here. Get your kids to help tidy if they are capable.
Go to bed as early as they do. Make sure your one emergency grandparent is aware of what is going on in case this gets worse. Best of luck.