I wore braces for 18 months and this was sometimes a problem when the wire would move due to my teeth moving; there was one time when virtually 10 minutes of walking out I could feel a wire so it was sorted straight away. Better than the wax they give you, you can use the wax that earplugs are made out of!! No joking, this was a tip from my orthodontist. They are covered in a cotton wool which you remove but this wax is so much softer when softened between your fingers and a great barrier between teeth and mouth.
I must say I was glad to get the things removed at the end but they were well worth putting up with when you see the result!