Just ran across this info too while I was searching something else;
"Fin Rot is often caused by several bacterial diseases such as Flavobacterium Columnare, Aeromonas, and Pseudomonas. [...]
If you catch Fin Rot early enough, you shouldn’t need to use antibiotics. But, if you do, you’ll want one that’s effective against gram-negative organisms."
Source: https://modestfish.com/fish-disease-guide/
Just a note, that article suggests Melafix, but I think Melafix is one on of the medicines not recommended for bettas, since it can coat their labyrinth organ and cause more harm than good. But this might help you select another antibiotic to try if he doesn't respond to the current treatment
"Fin Rot is often caused by several bacterial diseases such as Flavobacterium Columnare, Aeromonas, and Pseudomonas. [...]
If you catch Fin Rot early enough, you shouldn’t need to use antibiotics. But, if you do, you’ll want one that’s effective against gram-negative organisms."
Source: https://modestfish.com/fish-disease-guide/
Just a note, that article suggests Melafix, but I think Melafix is one on of the medicines not recommended for bettas, since it can coat their labyrinth organ and cause more harm than good. But this might help you select another antibiotic to try if he doesn't respond to the current treatment