If it's ich, you should see some tiny white spots that look like grains of salt stuck to his body or fins. Even if his colour makes them hard to see, they will stick out from the body or fin. If you see them, treat for ich.
Velvet might be harder to see at first.. keep a close eye on the fish and if you see any signs, begin treatment.
Bettas can handle salt, so you can add some salt to his tank now anyway, a good pinch is enough for 2.5 gallons, so double that. Sea salt, aquarium or kosher salt are fine, might make him feel better.