Hello~I am so sorry you are having this pain.
After doing a little research, here is what I discovered. A burning sensation in your feet (or legs) may be caused by nerve damage in the legs, also called neuropathy. Although many medical conditions can cause burning feet, diabetes is the most common. Most burning feet treatments focus on preventing further nerve damage and reducing pain. This is probably why the doctor prescribed the Gabapentin, I believe it is for relief of pain due to nerve damage.
Here is a link that might be of some help: https://www.webmd.com/diabetes/burning-feet-causes-treatments#1
Have you been checked for diabetes? If not, I would certainly ask your primary care physician for a blood test called "A1C" this test shows what has been going on with your sugars for the last 3 months, it is very accurate, in fact, some physicians are using it in place of the 3 or 6 hours glucose tolerance test.
Also, a Vitamin deficiency (vitamin B12, folate, and occasionally vitamin B6)can cause some nerve damage as can a low thyroid. I would also ask for specific tests for these as well as a complete blood count panel.
I hope you can get this resolved soon and feel better.