Welcome to the board. Camelia. This can be a wonderful place to get help from folks with years of personal experience. You might try posting your question on the Reflex Sympathetic Dystrophy thread. Regardless of what it is called, the burning pain is what it is all about.
To help answer your question, there are over 100 known causes for peripheral neuropathy. I personally advocate looking into the most common reasons while waiting for the doctors to do their thing.
Things they won't mention are nutrient deficiencies and the causes for them. B12 is chief among them as well as ALA. Inability to absorb any one of a long list of nutrients can cause your symptoms.
Food allergies can cause nutrient deficiencies. Gluten intolerance is chief here. There can be no gastric symptoms (such as pain) and there is no test for it.
To see if you might have a B12 connection, pick up some Methylcobalamin B12 and try a few tablets. You'll likely know within an hour.
Good luck in your search for your cause.

KYIMP