Hurt Axolotl

I have two axolotls. One is larger than the other by maybe an inch and a half. They have been living together for a little over two months. They have been great together but occasionally I find a couple of bits missing from my smaller axolotl's tail. He grows them back fairly quickly and I never thought it would be a problem. I went over to my tank today and a large piece of his tail was missing and it seemed like his leg was hurt too because he wouldn't use it. He stays very still I even thought he was dead for a moment. He leans on one side of his body and that scares me a lot. I believe it's because he doesn't want to put any pressure on his leg but I'm not really sure. I don't have a separate tank at the moment so I want to fridge him so that he's in very cold water and hopefully stress-free while he recovers. The tank is a 55 gallon and they have a large cave to hide with some pots on each side. Could the reason he's leaning to one side mean something else?

P.S. I fed them right away and they were both very eager to eat.

Not sure about the leaning, but you definitely need to put a divider up in that tank before you take him out of isolation!