is my fibromyalgia causing the soles of my feet to burn like fire?

It shouldn't . Fibro doesn't have that as one of the many pressure points of pain. My mother has been diagnosed with Fibro and she never has said there was any pain there, she tells of how she feels often. This condition has a genetic link so see if whoever in your family has this also would be suffering from the foot pain as described. There are feet pains often for those with diabetes I am aware, my dad has this.(Doesn't sound good but so far I 've been fortunate to avoid those).

I would talk to a podiatrist if this continues to be a problem for you. Best wishes that this is not something ongoing or reoccuring for you.
References :

FMS pain is at more than the TENDERPOINTS–it can be everywhere

BUT–it could also be plantar fasciitis or another foot problem
References :

The cause of fibromyalgia and burning sensations that you have are one and the same - a spirit (ghost). In antiquity, the symptoms of fibromyalgia were known as the invisible stigmata (effectively, bodily pain of a spiritual origin).

You can confirm a spirit by communicating with it. Use your thoughts (telepathy) by thinking, "hello, can you hear me?" You will likely hear it respond in your mind as if the response was your own thought. Upon realization that this spirit does exist, do not be mean to it. You symptoms (what it is doing) are for a reason. This spirit is the Holy Spirit found in the scriptures, and its presence makes you one of the saints spoken thereof.
References :
http://www.georgedstewart.com/index.html
http://www.georgedstewart.com/Library_files/Saints%20Past%20Present.pdf
http://www.georgedstewart.com/How_It_Is.html