It’s correct English, but extremely confusing. You could use it in spoken English, where your friend knows the context, but otherwise, it leaves too many unanswered questions: Does the “for free” also apply to seeing a doctor, or just to going to school? What is the connection — does the school offer free medical services? Is it like one of those barber schools where you get a cheap haircut and a clueless student gets to practice on you?
As far as language, it would be slightly helpful to use the word “either,” but really, the main issues have to do with context.