these are mostly tips for procrastinating but could apply:

prioritize according to urgency: do you have something to wear for tomorrow? do you have clean plates/cups to eat and drink? if one task needs attention first, that should be the only thing you care about. don't think about both at the same time.

and for that one task: if you can fragment it into small chunks and worry about only one chunk at a time that could help. you don't need to do the whole laundry, you just need a couple white undergarments washed today.

focusing on a small chunk could help minimize the size of the task in your mind and encourage you to get into it a bit more easily. usually starting is the hardest part so when you do a couple of clothing items, it feels insignificant, maybe almost silly not to finish it. i mean you're there, the laundry is there. "might as well" is a pretty strong motivation; how you might trick yourself to get to that part is the challenge.

some people use timers instead. like the five minute rule: commit to only do a task for five minutes. time it if it helps. again this should help minimize the task to just a five minute thing but once you're doing something for five minutes it will often feel trivial not to finish it while you're at it.

another one is a two minute rule: you don't even commit to doing the task itself. just commit to "get ready" for two minutes. that minimizes the task even more. getting the laundry basket ready, taking the hoover out of wherever you keep it and plugging it in, the simplest of things... once you're there you might feel comfortable starting at that point.

final thing, not about procrastinating but this might apply to your chronic illness:

once i tried learning to play the guitar, and had these audio lessons to get started. they put my mind at ease because here's how they opened:

Lesson One — If it hurts, stop.

sometimes it's easy to blame ourselves for feeling tired or even hurting through a task... and feel pressure to push through, only to risk feeling worse or injury