How are you? Burning sensation in the legs, hands and back can occur due to damage to the nerves in the form of peripheral neuropathy, which is a consequence of uncontrolled diabetes. What is your age? And are there any medical conditions for which you are taking treatment?
Vitamin B deficiency can also cause this condition.
Other causes can be guillian barre syndrome, Multiple sclerosis, occlusion of peripheral arteries and acute stress disorder.
I would suggest that you visit a neurologist and get an examination done. Also an estimation of blood sugars would be adequate.
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