Firstly: Why on earth should you be ashamed that you are single and living at home in your 40s? What is there to be ashamed of, particularly as you also have chronic health problems. It sounds perfectly reasonable and normal to me, and probably most other people as well.
Secondly: why are you assuming that your parents look on you as a carer in their old aage? Have you discussed that with them? Stop assuming what they are thinking, when you do not know.
I agree your mother sounds as if she has some illness and should go and see a doctor, but it may well be something quite trivial, but she cannot know until she sees a doctor - and the longer she delays this, the worse it may get. As for dementia, none of the symptoms you say your mother has sound remotely like dementia.
It seems to me you spend far too much time wondering and imagining everything that could possibly go wrong, but do nothing to confirm any of your conjectures.
Start by trying to find out the facts behind all your fears. Encourage your mother to see a doctor. Then consider seeing a counsellor to work out why you keep working up these fears but do nothing to resolve them. When you have done that you can move on thinking about what it is possible and practical for you to do to become more independent of your parents.