Hi Stephen -- I've had neuropathy for 26 years, and have had to take medications for it to help with the severe burning/tingling/zapping, etc that comes with it. I wouldn't necessarily call these meds "strong pain killers." You can get into very high dosages, if the lower ones don't help, but I haven't found that necessary.
The medications I'm on were originally for epilepsy, but as you know they found they helped neuropathic patients too. There are quite a lot of these medications that work. Right now I'm on Topamax and Lyrica. The combination of these two have helped me immensely as before, the pain was almost unbearable! Mne wasn't from an injury -- I had surgery over 26 yrs ago, for spine problems and the surgeries didn't work. So I was left with the neuropathy & severe back pain. My dosages are quite low compared to many people and I don't expect any increases any time soon. I'm having no side effects either.
You might talk to your doctor a little more about these meds, as they really might relieve the horrible pain you're in. I wish you the very best. God bless and take care. Hugs, Lee