Earlier this year, I went 100% Gluten-free for 60 days. I had been wondering this same question... Is much of my pain due to food allergies? So I committed to it for 2 months.
I'll be honest, I was kinda of disappointed. I honestly believed that my pain would reduce by at least 30%, but it didn't. HOWEVER, my IBS went away completely and I did lose 10 pounds! So it was beneficial in other areas.
The problem is that it didn't make a big enough difference in how I felt on a daily basis to make the trouble of being gluten-free worth it. When you're tired and hurting and emotional, it's difficult to also wrestle with a specified diet. (Not to mention that being gluten-free is an expensive style of eating.)
My recommendation is to try it for yourself and see if any results are beneficial enough to continue being g-free. It might not help with your fibromyalgia, but you may experience other benefits. I've now adopted a "half-of-the-time g-free" diet, just to stay thinner and keep the ISB away.
P.S. I have also found that alcohol and caffeine trigger flare-ups, but I can't kick the habit! Anyone else notice this?