Hi Uhura,
I was diagnosed by my family doctor!
Even though rheumatologists are often more aware of fibromylagia and what to look for than other medical practitioners, fibro isn't a rheumatic disease so not technically truly within their field of expertise. Rheumatologists classically treat diseases that affect the muscles, bones, joints, ligaments, and tendons, and while we feel all of those like crazy in fibro thanks to wonky signalling, the problem really lies elsewhere. That said, rheumatologists who have taken a particular interest in fibromyalgia can be really valuable to sufferers - but the extent of this can vary.
When it comes down to it, the key is getting in front of a doctor who is familiar enough with fibromyalgia to make a solid (as it can be) diagnosis, and fully willing and able to work through eliminating every other possibility. If you trust the understanding and diligence of your doctors so far, then I'd say that's good enough. That said, speaking to a new specialist in any field can sometimes highlight tests or treatment options that we hadn't encountered before - so there's always that to think about too.