Brief Answer:
Neuropathy could be the cause

Detailed Answer:
Hi
Thanks for writing
The burning sensation in your legs may be caused by any disease which interferes with the blood and nerve supply of the legs. Although many medical conditions can cause this burning ,Diabetes is the most common cause leading to nerve damage that is neuropathy.
In neuropathy, the leg nerves tend to become damaged first, at their furthest ends in the feet. This leads to tingling and numbness in the feet as well.
Do you smoke and take alcohol because there consumption may lead to burning sensation in feet.
Beside diabetes other common causes are-
Chronic kidney disease (uraemia)
Vitamin deficiency (vitamin B12 and occasionally vitamin B6)
Alcohol abuse
Low thyroid hormone levels
Vasculitis (inflammation of blood vessels)

My advice for you would be get following blood test done to find out the cause -
Fasting and after meal(pp) blood sugar test, Urine routine and microscopic test, Thyroid profile, Level of vitamin B12,Blood urea and serum creatinine level.
Take care and I shall be glad to answer any further query.
Regards

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