I've Got A Tail Biter

[damanax]

My boy Eventide has been biting his tail, I'm sure of it.
 
Before I went away on holiday I noticed that his tail was looking a little ragged but nothing to be concerned about. I replaced some of the silk plants with other silk plants thinking that he must have gotten caught on them. 
 
When I returned from my holiday I found that he had a big chunk missing from the top of his tail fin. I've been doing daily 50% water changes since I've been back to try keep the water clean enough for his tail to heal up but this morning he's missing a chunk out of the bottom part of his tail fin. There is no sign of fin rot or melt and its only the tail fin. I added a couple more silk plants and a barrel for him to swim through today incase it is just because he's bored
 
He is alone in a 20l (5.2g) cycled tank and it's kept at 26c. Stats are:
Ammonia: 0
Nitrite: 0
Nitrate 10ish (colour is a bit strange) 
 
Eventide has always been a nippy fish so I'm not too surprised but is there any particular reason bettas bite their tail's? Is it boredom, stress or something else? Is there any way I can get him to stop or is it unlikely?
 

 
 
 

 

[Wildbetta]

Tail biting is one of those things that is hard to point out a specific reason and say that is what you need to do to get him to stop.  There are some that bite because they are bored, some bite because they are stressed (water flow, tank mates, no hiding places, water quality, ect), some bite because they prefer to not deal with the big heavy fins that slow them down, and still others seem to have no reason to bite at all but still do.  Some tail biters will stop once the trigger is found and removed or fixed.  Others will never stop and will need to be watched constantly to make sure there is no infection at the bitten areas.  Keeping the tank warm and very clean while feeding good quality foods will help keep any tail biter from getting an infection.  

 

[damanax]

I think he may now have an infection. I've been changing his water every day trying to keep it clean and he appears to have stopped biting but that may be because he barely has any tail left. The last little bits of his tail have red through them and look a little bit like they're melting. Can't get a photo though, my camera is terrible.
 
The problem is that the only thing resembling an antibiotic I own is Melafix, which I've heard is bad for labyrinth fish, and I can't afford to buy anything else this week. Is there anything I can do? Warm, clean water hasn't been enough on it's own.