How should I deal with physical pain without medicine?

Many ways. I use many technques in my practice that are not based on pills. They can include physical therapy, yoga( my favorite), tens units, use of heat and cold to dull pain, mind-body techniques including meditation, relaxation techiques, biofeedback, acupuncture . These are just a few. If you see a pain specialist and tell them that you are interested in non pharmacological methods they can help.
Pain. Depends on the type and source of the pain. Finding and treating the cause is the most effective. Try healthy life style, meditation, hot soaks, ice packs, massage, mild exercises, support groups, prayer, fun and recreation if appropriate to your illness. Also certain vitamins, supplements and herbs may be appropriate.