In a case of mono do the white patches go away leaving you just a red swollen throat?

Yes. . With infectious mononucleosis( a viral illness), commonly there is a very sore throat with enlarged tonsils and white exudate in the crypts. Not uncommonly, this is treated as a strep throat with ampicillin; curiously enough, Ampicillin rx for mono not uncommonly causes a fine red body rash. At any rate, lots of fluids, saline gargles, tylenol, (acetaminophen) and adequate rest. Full time rest not needed.