Yesterday my betta had a small tear in his tail, which I thought he blew out from too much flaring, but throughout the day two more small tears appeared and his tail is looking ragged. This morning it doesn't look worse but it hasn't gotten better yet. I don't think it's fin rot because there is no discoloration and he is extremely active and eating very well. I think he might have injured the tail on a plant (that I removed) and then made it worse but swimming around so much (he only stops swimming at night when the lights are out). Either that or he's tail biting.
Water parameters are good, water is at a stable 80 degrees, he's in a 10 gallon filtered tank by himself and getting 25% water changes daily to prevent infection.
My question is, should I add a tablespoon of aquarium salt to the tank? People say different things, but I would really like to prevent infection and help the tail heal ASAP because he has a gorgeous tail.

Thanks!