@LovelyandTrying,
As far as your mum is concerned this is all very new, it just happened two months ago. I know this has been going on a lot longer than that, but from her perspective it's all new and she's still trying to come to terms with it.
Time does change people's attitudes and perspectives, all teenagers have trouble with their parents, even 100% straight teenagers who do well at sports and academic studies.
You'll have a better idea when you get to the end of your school career, either she will have accepted you or it'll still be a problem. By then you'll be old enough to move out and you'll know if you want to.
I'm straight, but I moved out the first opportunity I got, I just don't see eye to eye with my dad. Even now I can't spend more than a couple of hours in his company.
My son is transgender, he's 27 and still lives at home with me and his brother.
People are all different, but things have a habit of working themselves out.