I would see if your school has insurance for students (or, some association in the subject you're majoring or interested in; for example, I was a history major and the American Historical Association had insurance plans I could have qualified for, they don't have that anymore but I know my husband has IEEE insurance, as an engineer and member of that association) and then you could have your own? If you find a way to get your own health insurance, maybe your parents will reimburse you for it (or some of it) but, that way, you would control whose insurance it was so they would not receive any payouts.