Zebra Danio's Tail is Frayed?

I'm trying to figure out what is wrong with my zebra danio. I bought three new zebras after his buddy died about a week ago. Today I was looking at him and his tail looked like it had been cut off and was frayed. The place where tail meets body was more white than usual. The other danios are much smaller so I don't think they attacked him. He swims at the top of the tank, which I think is because of his tail, and seems to be breathing heavily. Is this fin rot? I've heard that introducing new fish can cause it, but they have been in the tank with him for almost a week and he has acted more lively than ever, not sick at all. He's about five years old, so I'm pushing it with his age anyways, but I'd really like to know what I can do for the poor guy.