I'm not the biggest expert on this Gunny, but I'll tell you what I think, and others can chime in. I'll also tell you where to go for the BEST advice on your question.
First, I feel ya about being confused and lost filing that first GWI claim and not knowing what the hell was going on. I did the same thing, and in fact it's been 9 years and my first GWI claim has been denied completely numerous times and is waiting in line for the first shot at the BVA. I have no doubt it will take many more years, and that I'll be dead before it's resolved.
I don't really see anything in your first claim that would connect to fibromyalgia (FM) that would justify you asking to reopen the claim with your new evidence. But you could tie it to your shoulder pain and sleeplessness, so if you want to try that, you probably could. If you don't care about the effective date, a new claim would work just as well. FM is a presumptive under 38 CFR 3.317 as a "Medically Unexplained Chronic Multisymptom Illness." As long as your doctor and you can show that it is FM and not something else (although that diagnosis from the expert rheumatologist would be much more helpful), that it is at least 10% or more disabling, and that it has lasted 6 months or more (chronicity), then it should be presumed as a CMI under this section.
That means you can claim it connected to the previous claim, if you can tie it to that claim, or file it as a new claim, since it has surfaced prior to the closing date selected by the Secretary of the VA (31 Dec 2021).
For the best help, go to the Self Help Guide at the National Gulf War Resource Center (NGWRC)
Hope this helps.
Dr. Dave
2017-ngwrc-gulde.pdf