@atlas2023 You've basically been on a newborn schedule for EIGHT MONTHS!!! Holy cow. I'm surprised you're coherent enough to even type!
You've don't a wonderful job these past months. I think the added stress of not fully understanding what is happening with your daughter and waiting for the diagnosis and treatment plan are taking a toll, on top of the sleep deprivation. Are you also the primary contact for her health and the one to take her to appointments? That's a huge job. I think once you have that figured out it'll be a huge stress gone and she will feel so much better and be able to sleep more. Don't feel bad about DH doing so much around the house, as you've sacrificed you're health the last 8 months without sleep.
From just a practical, how to get things done, standpoint:
Is there any wiggle in the budget to have a cleaning service come once per month? We have one and they do the main floor - master bedroom, kitchen, bathroom, family/dining room and the playroom. I can easily maintain it the rest of the time knowing they're coming back to do the bigger clean up. I also have a cordless vacuum and I'm much more motivated to vacuum (oh, you're in the UK, so... Hoover not vacuum!!) when I don't have to unplug and replug it in, lol.