Need a second opinion on Fibro. Diagnoses. Rheumatologist or Neurologist?

Either might. I know individuals in each specialty who are well-trained and have heavy experience in Fibro and others who don't meet that description. What you need to do is ask that at the point of calling for an appointment. Their office will tell you and might refer to one they know is best at that condition. Good luck - I hope it goes well.
Rheumatologist. ? 2nd opinion re Fibromyalgia from Rheumatologist or Neurologist. See Rheum: for years American College of Rheumatology has defined criteria for diagnosis & probably greatest skill using approved FDA Meds. My opinion: natural therapies w. greatest potential for "cure"; so also Alternative Medicine doctor: nutrition, myofascial & mindfulness therapies, biofeedback, PT, yoga, Cannabis, etc.