I personally was diagnosed by a rheumatologist after my PCP admitted she wasn't sure exactly what was going on with me. The rheumatologist only saw me once a year for "follow up", and the rest of the year my PCP did her best. I also paid out of pocket to see a "Functional Medicine" specialist who put me on a 6 month, high dose coarse of antifungals that would "cure" me (it didn't). Finally I got so fed up that I demanded a referral to a pain management specialist. Actually, I demanded a referral to a specific specialist who I had researched myself. That was 7 years ago and I'm still with the same clinic (Advanced Pain Management Center in Portland, Oregon). They were the ones who finally discovered what had put the fibromyalgia target on my back. Indeed it was my back: advanced degenerative disease that is probably congenital, combined with hyper-mobility.
My only words of wisdom are to remember that it is not the specialty a provider practices that makes him or her good at treating fibro; it is their knowledge about the disease itself and the appropriate treatment modalities. Ultimately you need to feel that your relationship with your doc is comfortable for you and that together you make a good treatment team (because treating fibromyalgia is a team effort, and you are the team captain).
Best wishes, and I hope you find a great doc to work with.