I think you know that you should say no. It sounds like you are mananging all the things you can handle at the moment and taking that on would be too much.
It is not selfish to take care of yourself. Like many wise people have said, if you aren't well you can't help others get well either. So I think it is very wise that you want to have some time for yourself. Like you said there are things you would like to do, more importantly you need to do, like starting therapy. Wanting to get help is in no way selfish.
I hope you get what I'm saying. I just want to really reassure you that it is okay to say that you can't take care of her right now because you have too much going on. You will still care for her and visit and such, but being her sole caregiver and housing her is just not something you can do. Besides, she is part of a large family so there are lots of people to help. If you say no others will realized that they can't depend on you for everything and as a result they will have to take responsibilty too.
You are not being selfish at all