The same thing happened to one of my recently acquired bettas
When I ordered him, I thought he was going to be a regular sized betta, but he turned out giant. So I "upped" his tank to your size (identical, but no gravel, filter, or rocks) and I have an OC condition with checking ammonia levels and such, so his temp and conditions are always ideal. I noticed when changing water, I removed the water about 50 percent and added water a little too rapidly and he got caught in an "undertow"-swirling. Ever since then his fins have been wrecked and now I "slow drip" any water going back into the tank.
I am waiting for him to heal, it's been about a week, and every time I look at him, I want to cry. It's not getting worse, and it's not rotting, but it's not getting better. Maybe I'm impatient?
They say constant water changes help promote faster healing. Also, it's my guy's dorsal, tail, and anal fin. If it was just the tail, maybe a tail-biter?
Curious to see what peeps have to say....