Ahhh Ali,
It sounds as if you have the weight of the world on your shoulders, when you should be carefree and starting to enjoy your teens and doing things that get YOU in trouble!
All you can do with Mum is keep encouraging her to see the doctor. I bet she is worried abut what may come of the visit, but it's better to know now so she can start treatment for whatever it is that is ailing her. You can't make her go. Just keep letting her know that you love her and you worry about her and that whatever it is, she and you, will be ok and will deal with it.
Let us know how it goes!