All the more reason to move someplace that has public transportation, so you can get around without a car. Can you move in with a relative who lives somewhere more convenient for a few months, until you save enough to get your own place?
I know what it's like, my mother was useless, although in a different way--she just did not want to be a parent and should not have had children in the first place. But I managed it by going to boarding school for a few years until I was old enough to drive, and staying with friends a lot over holidays. My friends were able to teach me to drive, carpooled to work with me after school. I took the regular school bus to school in the morning, then got a job near the school. After school, I would either go to work and then carpool home with my friends, or else go to college classes and sleep over at a friend's house that was close to campus. It was only a month or two until I had enough saved to buy a crummy old junker of a car, but it ran and then I was able to get around town, get to work and school on my own. Grandparents will think you are a sweet kid if you ask to stay with them for holiday breaks, and then you'll at least be appreciated for helping with chores.
Sorry to hear about your situation, but unfortunately some moms are never going to win Parent Of The Year Award. It's a hard lesson, but the only person who is going to take care of you best is YOU.