What research is being done on fibromyalgia treatment?

Probably much. I know from patients that many are helped my acupuncture, and anti-inflammatory diets. Exercise, some anti-depressants, and omega 3 also help. Best Wishes.
Lots. In the medical journals that i read, i see article after article about fibromyalgia. I believe it is a very active area of research.
All adjuncts. There may be ongoing studies for treatment of fibromyalgia. Without baseline cardiovascular activity (goal is 30 mins 5x/wk), regular sleep, and good nutrition, it is unlikely that any additional medications would be as beneficial. Acupuncture and medications that target nerve input like gabapentin, pregabalin, and duloxetine can be helpful adjuncts.
Britain. Re: research on fibromyalgia. British doctors have observed relationship between Joint Hypermobility Syndrome (JHS), fibromyalgia, & chronic pain. To my mind JHS potentiates delicate female pelvis joints to abnormal ligament laxity from childbirth & mechanical injury. Experimental evaluation of trigger points is important because these are likely the soft tissue peripheral pain generators in FM.