Did you rinse everything off really well? In general, you don't ever want to be in contact with soap or anything else that has chemicals in it before you touch or wash anything in your tank. For example, I never use soap to wash my hands before putting them in the tank, because those chemicals will linger on my hands. So it's very likely that he's experiencing skin irritation due to the products that have come into contact with his environment.
Secondly, because you rinsed everything with soap and then vinegar, you've essentially nuked your bacterial cycle. This means it's going to take time for your aquarium to build up its host of beneficial bacteria to process ammonia to nitrite, and nitrite into nitrate. So you need to be very, very careful with your axolotl because a build up of ammonia will only cause further skin irritation and problems. Another note-- if you're rinsing anything from decorations to your filter media, use ONLY used tank water or dechlorinated water. The minerals and chemicals in tap water will kill your bacteria and will cause your cycle to crash.
If it were me, I would find a nice-sized tub to put him in while your aquarium cycles again. It's just easier on both the axolotl and you. If you do daily changes on the tub your axie is in, you won't have to worry about his health as much as you would if you were to have him in the tank while its cycling. Do you know how to properly cycle your aquarium? Do you have a test kit?
Hope this helps! Good luck!
