I am 67 yrs young and was diagnosed about 15 yrs ago with fibromyalgia. Like you I didn't know who to go to. I had chronic migraines as well and already was being treated by a great neurologist. He said I needed to see a rheumatologist for the fibromyalgia and recommended one.
After several tests to check my ANA levels and other blood work he prescribed gabapentin for the pain that the fibro causes and then small amount of Adderall first thing in the morning to help me be able to work without falling asleep.
It really takes finding the right doctor or doctors that will listen and work together, then getting the right "cocktail "of medications to help manage the pain, exhaustion, and migraines, which fibromyalgia and migraines go hand in hand so I have been blessed with good doctors. Don't give up be assertive and find who will take time to listen and work with you to find what will work best for you.