You are not twisted, you are not disgusting or horrible.
You are normal, you are a victim, and being used as a slave no wonder you feel resentful.

Are there any jobs like residential ones, where you could live in. A hotel or something, you could save every penny you earn towards more education. They might be crappy jobs but at least you get away from home and get paid.
I don't blame you for hating grandma looking after this old woman is not your job.