This is the definition of a neuro:
Neurologist:
The neurologist is a specially trained physician who diagnoses and treats
disorders in the nervous system, whether caused by disease or injury. This
includes diseases of the brain, spinal cord, nerves, and muscles. Neurologists
possess a comprehensive knowledge of the neurological structures of the body,
including the cerebral cortex and its division into various lobes and their
individual jobs in making the body work as a whole.
Neuro's can diagnosis fibromyalgia too, just as a rheumy can. My neuro mentioned it to me a long time ago, but I wasn't ready to hear it.
Hope this helps.