If I got hit in my eye at school by a girl with a Frisbee and had to get eye exams and glasses, would she have to pay for them?

She might only be liable or responsible to pay if she were at fault. She would only be at fault if she were negligent, or unreasonably careless. In a case like this, that generally means either playing frisbee in an inappropriate place, like a hallway or classroom, or throwing the frisbee without even looking. But if she were playing frisbee in a field or yard and you were in the field or yard near where she was playing and the frisbee happened to hit you or you were actually part of the game, then she was doing nothing wrong or careless and would most likely not be liable. 
If she were liable and is a minor, then her parents or legal guardians would be liable. 
If she or her parents are liable and do not pay voluntarily, to get the money, you'd have to sue. In the suit, you'd need medical expert testimony e.g. a doctor to testify as to the extent, nature, prognosis, treatment, etc. of the injury, which be expensive...unless you have suffered some permanent sight loss or large medial bills thousands of dollars, it would might not be worthwhile suing even if she were at fault.