I can think of at least two stories where a character is taken ill and his roommate cares for him, but both take place at American universities, so that's not right. I can think of one story where a character is sent to school in Scotland, but it was more for discipline than hiding out, so that's not right, either.
The description sounded familiar, but maybe it was just the different parts that were familiar and maybe I never read the story you are searching for!
-Tom