Is my fibromyalgia be the reason the soles of my feet are burning like fire?

Unlikely: It sounds more like a peripheral neuropathy. Fm is not a cause of these symptoms.

Possible: That isn't a typical fibro symptom but since fibro represents an increased sensitivity to painful stimuli it is possible. Since that is a symptom of diabetic neuropathy check with your doctor for other problems.

Possible: Here we enter the frontiers of medicine perhaps, as there are cases of small fibre neuropathies confirmed on skin punch biopsies associated with fibromyalgia. But many other causes may exist, so this needs full evaluation. Diabetes may be one cause, but burning occurs with vitamin deficiencies, and even toxin exposure.