What is best way to treat burning sensation in arm and leg?

A burning sensation in the extremities sounds like neuropathic pain, which usually responds well to anticonvulsants like Gabapentin and Pregabalin. Also consider Duloxetine, which is an antidepressant. Please see a Neurologist if you haven't already for further workup and management.

Burning sensation as described, tend to indicate some Vitamin Deficiency syndrome; usually in the Vitamin- B Complex group. One could try he OTC B-Complex formulations or see the PCP/GP for Vitamin and other Nutrient Analysis with ultimate replacement therapy. But all these must be based on Healthy/ Balanced Nutrition and appropriate Exercising.