It doesn't look like velvet, but that's hard to see over the camera.
I would say don't use medications if you are not 100% sure on what it is.
What size is that? It may help to do daily, or every other day, water changes just for the sake of healthy and clean water for him. Aquarium salt is a beautiful thing too, I would highly recommend buying some. The smallest size is quite cheap.
I don't see a heater either...bettas are tropical and they're best in 77-80F.
Bettas also seem to highly appreciate crowded tanks. I have at least 8 large plants (it is divided, so 4 plants each side). For me, it alleviated stress and made them more comfortable. Like an actual "territory" that is theirs (they're territorial fish).
And what do you mean "condition twice a week." Do you just put in water conditioner? If so, what conditioner really is is for putting it directly into NEW water. When you remove water, and replace it with new water (water change!), you have to put the conditioner in the new water and then put it in. It doesn't go directly into the tank, unless the tank is 100% new water and your betta is not in there. The chlorine in tap water will kill him. Nearly all conditioners at least remove chlorine.
So for starters, buy a heater (if you don't have one), and do water changes every day / every other day. Also add in aquarium salt for him as well. Plants will be the next step down.