Check with a doctor to be sure but medications like Neurontin are infamous for their pain relieving qualities. It's actually an anti-seizure med that works on the receptors in the brain to decrease pain. The bad side is you do have to taper off it as quitting cold turkey can cause seizures but the good side is it's not addictive and it's not a narcotic. Like I said, check with a doctor as there's many more like that. I'll get yelled at if I start listing them here!! But they do exist and are worth trying if you don't want to go the narcotic route.
The only meds that are non-addictive you can get over the counter, like Ibuprofen and acetaminophen. I don't think muscle relaxers are addictive, except for Soma, at least in my experience, and can sometimes be helpful with neck and back pain. Ibuprofen or Naproxen is good for inflamation and muscle relaxers for spasms. I am not sure what else you can take or what you are looking for. Any Narcotic is potentially addictive, so if you have had problems with them in the past they would be hard to get off of.