Hmm, yeah. That looks more like fin trauma (filter damage or tail biting) than fin rot.
Do you have the Aqueon Mini-Bow and are you using the filter that came with it? Most of the filters that come with kits are too powerful for bettas. You could try another method of baffling or get a lower flow filter. I use the Tetra Whisper3i and it's very gentle.
As for his fins, if you add stress coat to his water, it'll help them heal faster, but as long as the water is clean, they'll heal on their own.
Either way, he'll be fine. Cute tank, btw :)