Is fibromyalgia a syndrome of some kind?

Yes. Since a syndrome is a combination of body alterations that fit a pattern, that is an appropriate term for fibromyalgia.
Yes. Fibromyalgia is label for constellation of symptoms including chronic pain four quarters of back, restless non-restorative sleep, depression, chronic fatigue & in some cases headaches, panic attacks, fainting, Irritable Bowel Syndrome, Endometriosis, Interstitial Cystitis & chronic widespread pain throughout body. Certain anatomical loci, which oft align w. ligaments & tendons tender to palpation.
Fibromyalgia. Fibromyalgia is a disorder characterized by widespread musculoskeletal pain accompanied by fatigue, sleep, memory and mood issues. Researchers believe that fibromyalgia amplifies painful sensations by affecting the way your brain processes pain signals.