I think it is more likely that something in your bedding, or the hair product you use (if your hair touches your neck while you sleep), or your pajama top (again, if applicable) or something like that is causing this. You could also take steps to make sure your neck doesn't get too warm overnight. This is just my opinion, but you might try changing those things one at a time to see if it makes a difference.
And, as with any new symptom that any of us have, it is always best to have it checked out by a medical doctor of one kind or another because there's no telling if it is actually related to fibro or not, and if not you need to know what it is.