I am so sorry you are in this situation right now, that must be very hard. Your parents are probably trying to raise you the best way they know how, but they are being deceived by a manipulative religion, so their decisions are not their own. Do your best to do all they ask, hopefully they will give you more priviledges as you show you are responsible.
It probably seems like forever, but in three years you will be an adult and will have more control of your life. Until then you need to do all that you can to prepare yourself for the life you want. If you have access to online resources, then focus on learning all that you can. If you dont, see if you can get books at the library. Art school is possible if you apply yourself. If you went to a regular school you could get help with this from a school counselor, but check to see if there is anything like that for home schooled teens. Do everything you can to prepare yourself to qualify for scholarships and grants.
We had a young lady here on the board who was home schooled also, and her mother didn't bother to teach her anything so she actually couldn't even read. She studied on her own and got her GED, and went on to college. If she could do it, so can you.
Good luck, I hope you get to follow your dreams.