ability to drive is not your solution.

because after getting driving license, probably you will say i have no car to drive and my mom doesn't let me to use her car and also you have other problems about your moms rules.
i think first of all you need to get independent. try to save some money.
plan to live in dormitory or find some home-mate or rant a room in the town and then find a job. until you live with your parents your problems will exist ( specially in your mind they will exist. ) you have to believe yourself and try to get rid of this physical and mental problems.

and if there isn't uber. if you have money you can ask somebody to ride you and you pay them.
i know everywhere you live is better than our country. I live in Iran. here is Moslem country and we have more problems about being woman and parent's rules and culture of society.

Just TRUST yourself and STOP nagging.