Hi Lilipad,
I go by the F.B.I rule when i assess a case of axolotls with swollen throat.
http://www.caudata.org/forum/showthread.php?t=60425&highlight=stomatitis
Firstly, i try to rule out foreign body. A foreign body is anything such as gravel, snail, shell or anything really that can get stuck in the throat. Are there anything in the tank that can potentially get lodged in the axie's throat? Are there fish or other species sharing the tank? Are you able to see if something is lodged?
Secondly, bloat can first present submandibular oedema (or puffy throat/chin). Bloat can be caused by many things - scepticaemia, organ failure (kidney, liver, heart), malnutrition etc. This condition when left untreated will cause quite rapid bloating in other body parts as well. The body and limbs will soon also get puffy.
Thirdly, axies can get a mouth infection called infectious stomatitis. This is caused by bacterial species such as aeromonas and pseudomonas. Normally axies with infectious stomatitis cannot fully close its mouth. The mouth will remain agape all the time. They will go off food or have difficulty prehensing or swallowing the food (food keeps spilling out/spat out). They will lose body weight and sometimes present with sores around the lips. Untreated, the condition can deteriorate and can cause fatal scepticaemia. Infectious stomatitis is also transmissible to other axies.
In view of the possiblity of an infectious disease, i would recommend you isolate your sick axie. Keep this axie away from any others. The best way is to fridge your axie as that can help with its immune system, destress it and also permit for easy monitoring. Meanwhile, i would recommend you feed small portions of blackworms, chopped earthworms or small bits of pellets. Try to keep the food soft and small to facilitate easier feeding. You can try leave it this way for 2 weeks to assess how its going. If you don't see any improvement or worst still, signs of deterioration, i advise you bring it to your vet for diagnostic testing and treatment. Infectious stomatitis will definitely require antibiotic treatment.
http://www.caudata.org/axolotl-sanctuary/Fridging.shtml
Cheers.