Cherry barb; fin rot/other or just tankmate aggression?

[Georgia99]

So I got three cherry barbs from my friend last week as she was unable to care for them. However, the day after I got them, and I got a proper look at them, I noticed one of the fish seems to have quite a lot of its tail missing?

I thought it was just the others nipping at it but it looks too bad to be done by such a little fish! Almost the entire top part is missing. I also noticed a part of the dorsal fin is missing too although it's harder to see and I'm worried it's some kind of disease

I've attached the best photos I could get

 

[Georgia99]

Also, I know they can be more aggressive in smaller groups but can they be that aggressive? I was planning on getting a few more in the next weeks or two