First what are the tank parameters? Ammonia,nitrite, nitrate ph and temperature?
Second are you using filtered water all the time? Axolotls like harder water and filtered water is to soft for them so unless you are adding dissolve minerals to the water it would be to soft for them. Tap water with a dechlorinator is perfect unless the tap water is way to hard/has other issues but regardless you would needto be adding things to the filtered water.
Is there a lot of water flow in your tank? If your axies skin is peeling it could be from high ammonia or it could even be from using the filtered water.
You should really test the water i suspect maybe even a low ph maybe? If the water is to acidic it could be damaging the slime coat.
Maybe using a black tea bath instead of salt will help soothe your axies skin more. Remember salt bathes are used primarily for fungus so unless you start seeing some white fuzzy stuff growing you should probably avoid it. Salt bathes are pretty stressful on them.
Fresh cool dechlorinated water changed daily would probably be the best thing till we can figure out a cause for what is going on. But use tap water instead