Varies. A rheumatologist is the specialist who would be most familiar with this disease and it's treatments. This disease can be difficult to treat, but there are a number of medications available, with varying degrees of effectiveness for fibromyalgia.
Various. Fibromyalgia is a mulifactorial disease and requires a variety of approaches. Within the orthodox medical world, rheumatologists do most of the diagnosis and treatment. Naturopathy is the genre of complementary therapies to be advised. See both specialists contemporaneously and ask them to judge each other's suggested therapies.
3 meds, specialist. There are 3 indicated medicines for treating fibromyalgia: lyrica, Cymbalta and savella (milnacipran). However, they are all different and don't work for everyone. Finding a specialist who treats fibromyalgia is tricky. There are very few rheumatologists like me who enjoy treating fibromyalgia. Most will see you once, confirm the diagnosis, and then never see you again. Find a doctor who enjoys treating fibro.