Student Exchange Programs

So i have studied in an english school in turkey untill class 10 which has nothing to do with the turkish system after that i switched to a turkish school and im in class 10,but i am not planning to go to uni here i really want to study abroad i dont think ill have visa issues because im half portuguese thus possesing an eu passport what i want to ask how would i join a university in europe or in the us but i dont want to be an exchange student or something.
I am planning to study medicine and be a doctor,are there any diffrences in private universities?