I don't think you need to dose meds for something like this. Clean warm water is all that is needed to heal stuff like this. Medicines ending in "fix" (melafix,pimafix,ect) have the reputation of coating and damaging the labryth organ so they are not recommended with bettas. It looks to me like a small tear in your betta's tail and the driftwood is probably the culprit. You might want to run a stocking over it to see where the sharp edge is and find a way to smooth it.