Salt baths are indicated for fungal infection as well as external parasites. They are best used in conjunction with fridging.
http://www.caudata.org/axolotl-sanctuary/Fridging.shtml
With fungal infections. I would recommend you give two salt baths per day for 3 days. Space the interval period as evenly as possible, ie. - 8 am in morning, 8 pm at night. An hour or two off is ok. During these baths, the axie will attempt to struggle a bit. This is normal.
Basically just prepare a tub of fresh dechlorinated water and dissolve 2 to 3 flat teaspoonfuls of non-iodized salt per litre of water. You can use salt such as
kosher salt, freshwater aquarium salt or sea salt. Do not use table salt. You can then place your axie in the salt solution for about 10 minutes but no longer than 15 minutes per session. Excessive salt solution soaking can cause damage to the axie's gills and skin. Have a look through this article as well.
http://www.caudata.org/cc/articles/salt.shtml
If you can gently tease off any flaking/peeling lesions that is also fine. You can do so gently with a cotton Q-tip. Roll the Q-tip towards you to gently lift away at the lesion rather than prod at it or roll inwards which can damage the skin.
Monitor the progress and response of the axie during the salt baths. From the 4th day onwards, reduce down to once per day until the end of the week. Continue to monitor. I anticipate a marked improvement by day 3. If by end of the week, the salt baths and fridging did not improve the condition, again a vet appointment will be necessary.
You can also prepare one or two bottles (1 or 1.5 L bottle) of salt solution in the fridge. The most convenient time to do salt baths will be during your daily water changes. As the salt solution is fridged, there will be minimal thermal stress.