Definitely fungal. Do what has been advised above, but on top of that you should try a tea bath. Put a teabag in a cup, boil the kettle, pour the boiling water into the cup, let the tea cool, then add it to your tank. The tannins from the tea will act as an anti fungal remedy, and will not harm your axolotl whatsoever. In fact, they'll probably welcome the darkness.
The tea is removed gradually over time when you do your weekly, 20% fresh water changes.
Another thing to note is temperature. Too high and it causes stress, which will contribute to swift deterioration in health. Don't exceed 22C, but ideally you should be around 18C.
If you don't already, it's vital to measure your water quality each week to make sure that it's safe. I use the API Freshwater Master Test Kit. It costs around ÂŁ30, but it's well worth it. You get hundreds of tests-worth out of it, as opposed to the cheaper water testing sticks which only last once. That, along with how you only test once a week, and you'll find that it lasts you practically forever.
When testing your water quality, there are certain things you should be measuring. These are: temperature, pH, ammonia, nitrites, and nitrates. These are the ideal parameters:
Temperature - 18C - 22C (aim for 18C)
pH - 6.8 - 7.4
Ammonia - 0 ppm
Nitrite - 0 ppm
Nitrate - 40 ppm or lower
Too much ammonia will poison you axolotl, as will too much nitrites and nitrates. Nitrates are good for friendly bacteria, however, so it's always good to have a little bit.
Also, I'm sure you're aware, but water taken from the tap needs to be de-chlorinated, otherwise you can poison your axolotl. Either use a water de-chlorinator available in most pet shops, and even supermarkets (I've seen some in Tesco by Bob Martin), or let the water stand for 24 hours. Letting the water stand allows the chlorine to evaporate.
Let us know how you get on.