I have the same burning pain and have seen many foot doctors who don't seem to know exactly what is causing it or how to treat it other than pain meds, which I am reluctant to take. One doctor said that the only solution would be to cut the nerve in the foot, but that would actually cause more harm than good because cutting the nerve means that I would no longer have ANY feeling in my feet at all, including "good feelings." That means if I cut my foot on a piece of glass or a sharp object, I wouldn't feel it and I would not notice that I could be bleeding to death.
So living with this constant pain is the alternative. I am 59 and I dread having to live the rest of my life in this pain.