If the end of an orthodontic arch wire (see diagram) is poking in the back of the mouth, attempt to put wax over the area to protect the cheek. Call the orthodontist to schedule an appointment and have that clipped. If you are uncomfortable, make sure you inform the orthodontist.
In a situation where the wire is extremely bothersome and the patient will not be able to see the orthodontist immediately, as a last resort, the wire may be clipped with an instrument such as fingernail clippers.
Reduce the possibility of swallowing the snipped piece of wire by using folded tissue or gauze around the area to catch the piece you will remove. Use a pair of sharp clippers and snip off the protruding wire. Relief wax may still be necessary to provide comfort to the irritated area.