I have no idea what is causing the pain but my experience with neurologists is they like to run tests and then have you come back for more with no answer to the problem. Go to a rheumatologist. That's my advice.

There was an article written Dec 23 2020 in Fibromyalgia Community called: Fibromyalgia Mystery Solved!
that stated:
"scientists have now revealed that the main source of pain stems from a most unlikely place -- excess blood vessels in the hand."
They found an excessive amount of nerve fiber called arteriole-venule (AV) shunts.
The ...."blood vessel ending contributes to our conscious sense of touch and also pain." The research done involved taking skin samples. Perhaps this is the theory your neurologist is going with.

I have small vessel neuropathy caused by frostbite decades ago. Mine has become Renaud's syndrome. Before anyone panics, you have to get frostbite as a cause. I had a very severe case of frostbite.

My only experience with a neurologist is after I had what was thought to be a mini stroke. He looked at my test results and determined that it was an occular migraine. I've had many occular migraines since. He also told me I had 3 degenerated disks in my neck and not to see a chiropractor.

Definitely see both a Rheumatologist and Neurologists

I've heard of small vessel neuropathy in the hands for people with Fibromyalgia. Getting a Fibromyalgia diagnosis should come from a rheumatologist. That specialist will do blood tests to rule out other possibilities. I had blood tests, but the pressure points test first.
Good luck, take care.