Being an opiate addict, I had to get out of the frame of mind of, "There must be something I can take," and had to replace it with, "There must be something I can DO." Once pills were no longer an option, I still had a lot of pain, still do have pain, but nothing I can't handle. So, what do I take to deal with my pain.
Physical therapy, yoga, message, TENS unit, good nutrition, drink lots of water, and I work on inner peace every day. I have much less pain than I did, even on opiates, but it took more than a year to heal all the damage I had done on opiates. One major factor I had to change, I don't' push through he pain anymore, like opiates helped me do. So, the main thing I take for pain is breaks. I have 3 permanently fractured vertebrae in my back, mild scoliosis, and degenerative arthritis, so I get pinched nerves that are the worst pain I have ever felt, even worse than my broken jaw or fractured arms. Knowing my limits has helped me stop pushing myself to that level of pain. I always have some pain, but my natural pain killers finally started taking care of that, enough I can function.
I don't know your story or what you have tried so far, but pills would be my absolute last resort. I'd have to be on my death bed or near death to take any kind of prescription medication. Fentanyl is the only narcotic that will work, they are the only opioid stronger than subs. OTC's are fine, but deal primary with symptoms and not cause, so may not be addictive, but we can become dependent on anything.
Back pain can be a side effect of suboxone use.
You could try chiropractic care,physical therapy, massage.
Have you been attending doing counseling or substance abuse support groups?
Have you considered tapering off of the suboxone yet?