FasciculationsMuscle twitching are sometimes described as annoying but rarely painful. I wonder if in the muscles that might be fasciculations could be experiencing cramps. In syndromes with fasciculations, cramps can occur and can be quite troubling. There are no treatment for fasciculations (and as they are not troubling, none is needed), but frequent and disturbing Cramps can be treated with medications such as Quinine, phenytoin, or carbamazepine. Obviously, these medications have there own side effects, so if you suspect these are cramps, your neurologist would be able to tell you more.
Lastly, your question re: Fibromyalgia. As I've stated before on this forum, a neurologist is often the wrong person to ask about fibromyalgia, because many disagree with rheumatologists about it's incidence, diagnosis, or even its existence. It is a vaguely defined syndrome with little objective findings. That being said, descriptions of fibromyalgia are generally not the cyclical course you describe.