It sounds just like external parasites. Bettas with external parasites frantically rub up against anything, which usually just rubs more parasites ONto their body. Doing a water change and adding aquarium salt is good! Try adding a pinch of salt each time you change his water from now on, as that usually prevents parasites. Add a drop of Aquarisol, or if it seems like the parasites are advanced add Clout. You may or may not want to throw away any gravel/plants that were in his old tank and *thoroughly* clean the tank he should recover pretty easily!