I have had this happen when shooting a short bow that pinched. It does take a while to get the feeling back, nerve tissue heals slowly.
Undoubtedly you compressed and injured the nerve, but it will recover if you do not reinjure it. The doctor will tell you the obvious: to lay off shooting the bow and give it time. In the absence of more severe trauma, I would be surprised if it was treated more aggressively unless it persists for quite a while.
You might consider a tab with some stiffness to it to shield the finger, and limit the number of shots in your practice sessions until you build up a callus. That's what helped me. Good luck.