It sounds like it could be related to your neuropathy. Do you have any pills for it, like Gabapentin (Neurontin)? Do your pills help your burning back? What is the cause of your peripheral neuropathy? Have they found it? What have they checked for? Thyroid issues? Diabetes? MS? Injury or pressure on your nerves?

Perhaps you should get a second opinion. It sounds like it's your neuropathy is getting worse. If they haven't found the cause, maybe you should see if another doctor can. It might be unusual, but it's not unheard of. Do an internet search for "burning back sensation" and you get results for it. It's not that strange.

If another neurologist can't help, maybe you should see your GP and ask what other specialist you should try. Good luck.

I have neuropathy as well due to disc disease and pinched nerves..My left shoulder blade burns like crazy as does my lower back and hips and heat or cold even light touch drives it crazy..What has helped me some is (lidocaine patches) it helps to numb the area and this brings some releif..It does hurt putting patches on as they are cold but it lets up rather fast..Never know it may help..