Help may baby snapper!?

Recently when i moved him from his old tank to a more "realistic" enviroment with veggetation stones twice the size of his head..a filter..a basking dock and a uvb light, no heater cause they do not bask. And hes actually ALOT more actice and actually eats like a little pig he would barely eat in his old tank a 20g with just one hide. I felt bad so i took him to his new enviroment but a week before i took him out i had noticed he had a kink at the tip of his tail, i did'nt think anything was wrong i thought it would realign but instead it fell off. And i think it may be infected. Its been about a week since it fell off and now a nother piece of tail is turning whitish and i'm afraid that the infection will slowly kill him. he is still interested in food. I can't take him to the vet because he is just to fragile the vet would only do worse. Well im very worried. Is their any medicine i could put in there to kill the infection? It could be skin from when it when it fell off or it couldbe