On the Sleep Disorders Board, you will find a post by rainb0w that reads, "can't move or open your eyes?" In this post, it talks about sleep paralyzation, which is very similar to what you described. There are also some other references to other threads on sleep paralyzation within that post. You can read them, as well. Hope that helps!
P.S. I've experienced this, too. In my case, it is related to my Restless Legs Syndrome. I'm not saying that you have this syndrome, but it (and other sleep disorders) is closely related to fibromyalgia, so you might think about talking to your family doctor or rheumatologist about getting a referral to a sleep clinic. Good rest is crucial for someone with fibromyalgia. Now that I've gotten my Restless Legs under control, my sleep has gotten better, and my fibromyalgia pain has decreased. It's worth considering, and in my case, my insurance paid for my sleep study and my visits to the doctors at the sleep clinic! Good luck!