Craig
I have been avoiding back surgery for herniated discs this year by going to physical therapy. The word I get from the PT is this - if it hurts, but doesn't get worse after, go for it. If it gets worse from the movement, back off. The pain from my injury feels like a muscle cramp in my legs. Actually, my leg muscles are fine, it is only a phantom pain from my L5 disc hitting a sciatic nerve. In your case it sounds like your injury is higher.
My doctor steered me to a great physical therapist, and if your insurance covers it, it is worth a try. Mine encouraged me to use my bow, and so far, so good.
In my case, he told me that the movement was good, sort of a "no pain no gain" scenario. As long as there is no weakness or numbness, it is just a matter of ignoring the pain.
Good luck on your recovery, and you might want to be referred to a neurologist or spinal surgeon by your family doctor. You will also learn a lot by talking to other people going through physical therapy.
(Also there is no shame in using a 30# recurve to perfect your form until you can heal a bit more.)