Hi Arashi
Finrot is a bacterial infection caused by either Columnaris or Aeromonas bacteria. Or, as is often the case, by both of them at the same time.
It takes hold when a fish's immune system is weakened by any or a combination of the following factors: overcrowding, high nitrites, uneaten food in the tank, low oxygen content of the water, infrequent enough water changes, sudden increase in temperature. It's not unusual for a betta to arrive from the lfs with a case of it since they undergo horrible conditions while they are being shipped and often while they are there.
I recommend Kanamycin which is an antibiotic sold as Kanacyn by Aquatronics or KanaPlex by Seachem. It will treat both kinds of bacterial infection. Or, you could use Maracyn, it will treat Columnaris, but you will need Maracyn2 to treat an Aeromonas infection. Since you cannot tell them apart readily, use them both at the same time. (KanaPlex is not a very expensive medicine. That's partly why it's my first choice to use.)
While you are medicating him, keep the water at a constant temperature no higher than 75 degrees and if possible, add an airstone to keep the surface of the water slightly in motion which will add oxygen to the water. Both these things will make it more difficult for the bacteria to reproduce and so make the medicine work more effectively.
Follow the instructions on the medicine and give it for the fill course that is recommended even if the fish appears to be better before that.
Good luck. I hope your betta gets well soon.