A good doctor will treat the insomnia, the pain, the exhaustion. A lot of the brain fog comes from the sleep deprivation.
There is a sleep medication that helps fibromyalgia but most doctors won't prescribe it and its crazy expensive. It's the only medication that causes the body to actually sleep properly. OMG it's amazing! I used it for over a year then my insurance quit covering it.
A lot of the problems from fibro come from the sleep disorder. If you can treat the sleep problems, you'll feel a lot better. Have you ever had a sleep study done? If not and you have insurance, ask your doctor about it. It'll tell you exactly why you're not waking up refreshed. Mine showed that I get no stage 4 sleep, the deep restorative phase and cycle in and out of REM too often.
The cold issues could be related to your thyroid. Even if your bloodwork is normal, your thyroid can be underfunctioning but you have to have a doctor who's willing to try the the medication.