How do I know whether to go to an orthopedic surgeon or another therapist for non surgical pain management evaluation?

Additionally. You can also see a sports medicine specialist (doctors with training from internal medicine/family medicine/emergency medicine/pediatrics/ or physical medicine and rehabilitation). Or you can see a physical medicine and rehabilitation doctor. If you are adamantly not interested in surgery, then you might consider the other options first.
Talk to your doctor. You can always see an orthopedic surgeon for a musculoskeletal problem. Most of what we treat is non-surgical, and appropriate non-operative recommendations can be discussed. Coordination of care with physical therapists or pain management specialists can be arranged.