The nerve pathways get confused, and tell the brain the problem area is the teeth
That's one way to look at it, Ginge ! I find it easier to explain this to lay folk by saying that the longer roots of some upper-jaw teeth actually protrude into the air-filled maxillary sinus cavity directly above ! That more easily explains the apparent pressure sensitivity of teeth.
Either way, yet more reason for NOT flying when you have any kind of URTI ! !