Hi Tom,
I think Geosheets was wondering if the axolotl could have a rock in its mouth.
I have seen swelling like this two times before. The first time, there had been an injury (the axoltol got a mouthful of catfish spine) and the second time, the axolotl had an infection (chlamydia). In the first case, the swelling went away on its own; in the second, the swelling went away after the axolotl was given salt baths with iodine, but returned immediately after the salt baths were stopped; an antibiotic was necessary to do the trick.
These are only the two similar cases I have seen, and my experience is limited. If it is at all possible for you, you may want to take the axolotl to a vet and have them do a blood test for infections.
Good luck to you,
-Eva