What could cause me to have two flat red spots behind my right ear? Not painful or itchy

Most commonly. these would be little patches of inflammation/irritation, but without being itchy it is less likely to be an allergic or inflammatory reaction. Perhaps they are petechiae which can result when tiny blood vessels called capillaries burst under the skin. They can be caused by injury/trauma. OK to watch for a few days. If more develop, become painful or irritated, see your Doctor/Dermatologist.