Hi Julia53 and welcome
Fibromyalgia is absolutely real. Researchers currently understand it as a dysfunction of the central nervous system. Normally your spinal column and lower brain filter out pain signals that aren't important, like when you stub your toe. It hurts really bad at first, then the pain fades away. That happens because of a biochemical mechanism that turns the pain off (or at least turns down the volume). In fibromyalgia that mechanism is broken and the spinal column and lower brain wind up amplifying pain signals. Sometimes normal sensory signals get changed into pain signals too.
We don't have a good way to directly measure how that mechanism works, so there isn't an irrefutable test. But that's true for a lot of conditions, including lupus and ms, which are notoriously difficult to diagnose. Unfortunately there is a lot of prejudice against fibromyalgia for whatever reason.
There is new research coming out every year. Learn as much as you can about fibromyalgia. Find the things that help you (we are all a little different in what works for us). Ask lots of questions - I learned a lot on this forum.