I had exactly the same issue! GPs ran a few tests and couldn't figure it out. They labelled is as fibromyalgia, even though I didn't fit the criteria. I pushed to see a neurologist, who ran a few tests and couldn't figure it out - he also labelled it as fibromyalgia, even though when I questioned it he admitted he knew almost nothing about it!

There was a lot of back and forth, with GPs and neurologists being really dismissive. I forget how long this went on for, but a couple of years at least.

So I did my own research over a long period of time. I found only a handful of other cases, but with the symptoms I came to the conclusion that I must have small fibre neuropathy. I pushed the neurologist, who grudgingly did a nerve biopsy, which confirmed small fiber neuropathy. He stopped being dismissive after that.

For pain, I ended up with a similar situation. I tried gabapentin, pregbalin and all the usual things like topical capsicain, TCAs, SNRIs, diazepam, opioids etc. They either didn't help, couldn't be tolerated, or caused more problems. Within the public healthcare systems, the list was eventually exhausted, and they weren't interested in trying anything else. They didn't believe how bad the pain was, and were unwilling in any case to go beyond their list of standard treatments. In the end, I paid to see a private pain specialist, and eventually found ketamine to be really helpful - not just with the pain, but my mental ability to live with it.