What a shock that would have been!
I'd get him out of the tank (away from the other) for the time being and quarantine him somewhere cool, quiet, and dark to try and relieve/reduce stress. Don't go crazy checking on him a million times, you'll only add to his stress.
The skin peeling off is probably skin that died when it dried out (I think.) I'm assuming we'd rather have it peel off than stick to the body and have it rot there, so I think peeling is healthy and to be expected. I haven't had it happen with my axolotls, but I did have a betta jump out once. He was *crispy* when I found him and somehow managed to survive- lived to the ripe old age of 4.
Some might disagree with me, but this is a case where I would use a bit of melafix. Even though it's liver-toxic in the long term and irritates the mucous membranes, you probably want to do just that right now. The logic being: the skin dried, and mucous membranes have obviously been damaged/scraped/generally disturbed by his ordeal flopping on dry land. Any mucous at this point is probably a bit lacking. By introducing an irritant, you'll stimulate an over-production of mucous. Since this is what protects your axolotl's skin, you want to help him recover his protection as soon as possible. So- I would use some melafix, but at less than recommended strength.
If he's still alive tomorow start thinking about anti-bacterial and anti-fungal remedies. Have these on hand in case they're needed- you don't know what kind of bugs he could have picked up from the floor!
Hope that helps a bit, and I really hope he recovers!
