Can fibromyalgia cause throbbings in different parts of the body like rapid quiverings that last for several seconds and it occurs 6 times or more/day?

No !: The limits of the diagnosis of fibromyagia is not clear but throbbing is not supposed to be a major complaint.

Maybe: What you are describing sounds like muscle spasms. Muscle spasms are a common complaint that fibromyalgia patient's have. However, only a physician who specializes in fibromyalgia can determine if these problems are from fibromyalgia and not something else. See a specialist.