I've never had a betta that bit his own tail, but since I'm in the process of treating 2 new bettas for fin and tail rot.... Yes, that's what yours has. My red fish arrived 3 weeks ago yesterday... I bought a red halfmoon and he looked like a crown. After the first week he was laying on the bottom and wouldn't even move to eat. When he did move, little pieces of his fins would break off. I headed straight for our local fish store and got some "Betta Revive". Within a couple hours he was swimming again. My blue fish's fins and tail started splitting right after the red started to "revive", so he's now under treatment too. They were bought from a reputable dealer... but he only guarantees live delivery... The "Betta Revive" prevents, controls, and treats Protozoan diseases, Bacterial diseases, and fungal diseases. I don't know what brand would be in your area, but look for something that will treat like this. My guys are like new fish after only two treatments.