I've been having pain in my right hip. It feels like it's pulling. Is this to do with my fibromyalgia?

It may be part of a general problem with your muscular skeletal system, which is now affecting your hip.

It is common to find that a small injury has caused someone to hold themselves differently to compensate, and this can throw the whole muscular skeletal system out, resulting in a great deal of spreading pain, as the oxygen supply to the various areas is diminished.

I would suggest consulting a physiotherapist or someone who is competant to do myofascial release, to find and resolve the initiating injury.