I do get frustrated with posts that pass the buck back to the parents.
I can not begin to imagine how frightening it must be when you start to lose your independence, you constantly don't feel well and you are closer to dealing with your own passing and perhaps that of your partners. For some people, it is not an option to say deal with it yourself despite how much it may make you feel like you are drowning. Many want to be there for their parents at this stage in their lives and would regret it if they were not.
In terms of your parents, you need to ensure that they are getting everything they are entitled to. This always gets a lot of criticism when people mention it but is the parent who is not mobile and requires assistance with other care elements entitled to CHC funding? If you phone Beacon it is a free helpline and they are excellent and will talk you through whether this is an option. We used them when we were going through this with my Mum and they were really helpful. If they are entitled it will ensure that the correct care package is in place without any top-up required.
https://beaconchc.co.uk/
We also used an Elder Care Consultant, she helped us get all the benefits that both parents were entitled to. She was also our advocate for the CHC meeting. Whilst she was expensive she more than paid for herself.
I also do understand the problems with siblings not doing their fair share. This is one you have to leave alone. No amount of talking will get them to do their fair share so stressing about it will only increase your stress, you have to find a way to put it to the side.
You don't say much about how much your family help out but I found with my parents and other people I know in the same situation; it becomes about processes. What can you put in place to make it all a bit more efficient so that time you crave on your own or with your family becomes possible? It also becomes about what is important and stop anything that is not.
Maybe the first step would be a family meeting to work out what can be done. I have found that teenagers can step up in these situations. My My 18-year-old niece when my Mum was sick was amazing. I know of other families and their teenage kids have and are incredible. As a family assess what can be stopped, what can everyone help with and is there something that can be put in place or changed that you have not thought about and are blind to because you are so deep in it?
Once you find that time you need to make it sacrosanct so everyone knows you can not be disturbed.
I am with you OP this is such a hard time in your life, I am going through it and I can't offer much more advice other than you are not alone.
Good luck.