Hello and thank you for your question.
Burning feet can be due to condition called peripheral neuropathy. Peripheral Neuropathy occurs when there is damage to the nerves.
In order to treat neuropathy cause of this condition is very important to know.
If you have history of diabetes or any auto immune process or deficiency in vitamin B12 can cause Peripheral neuropathy. Sometimes it can be idiopathic neuropathy where the cause can be unknown.
Any injury to feet can also cause neuropathy and so is the compression of the nerve in lower in the lower back can also give burning.
I would suggest to see a neurologist who can order EMG nerve conduction test and also order blood test to evaluate the deficiency of vitamin b12.
Usually for this symptom medication like neurontin or pregabalin is prescribed. Using ointment called capsaicin can also help with the medication. Lidocaine patches can also help to relieve the symptoms.
Please get back to me if you have any further questions. Thank you.