Betta Fish: Help! Fin health!

I need your help! This is my beautiful boy Astarion Da Fish. We’ve had him for a week, and yesterday morning, we had a spike both of ammonia and nitrite (0.5ppm for both) after an emergency water change, the parameters are back down to 0ppm for both, but we’re monitoring it daily.

While doing some tank cleaning, I had a close look at his fins (his dorsal and caudal in particular), and I’m not sure if they’re damaged at all, or if he’s starting to get fin rot. This is my both my partners and my first betta, and we really want to keep him in the best health possible. Please help!