Do you have high arches, by any chance? I have what my hubby calls 'Barbie doll feet'--very high arches, and yes, they do cause problems.
I try to keep them warm at night by wearing soft socks. I use soft arch supports (from Wal-Mart) during the day, along with elastic bands that go around the arch. They seem to lift the feet and provide some support.
Would your shoes during the day be an issue--heels too high or no heel, maybe? I have to have arch supports or my feet are 'sunk' (literally).
Foot pain seems to be a common fibro complaint. If you type 'foot pain' in the search box (above), there are lots of posts from this forum, though I'm not sure there were specific problems like you mentioned.
I hope your feet are better soon. That can be absolutely miserable! Wish you the best.
ETA: I sometimes get very achy legs overnight, and have no idea why. If it's anything like your achy feet, I know how terrible it feels. Massage helps me a little when that happens.
Though I dislike meds, Neurontin (gabapentin) has helped with nerve pain in my feet. Muscle rub creams sometimes help, too.
Now that my feet are in better shape than some other years (should I knock wood? LOL!), I walk a lot more--something I didn't used to be able to do much at all--and it has gotten better. I'm sure it's helping my circulation, too. Are you able to walk a lot during the day, and do your feet bother you at all then?