Depending on the circumstances, probably. They couldn't take action that would adversely affect either or your educations, i.e. they couldn't prevent you from taking Calculus because your girlfriend is in the class and they're trying to keep you separate. But they could certainly reassign your seating and prevent you from having contact on school grounds.
Curious what would prompt the school to take such action. Passing notes in class? Snogging in the hallways? Isn't high school grand?
