Burning sensations are usually a sign of nerve problems. These symptoms can be caused by the 'entrapment' or compression of the nerve that travels over your elbow and then into your fingers (ulnar nerve entrapment). That entrapment could occur at the elbow or as the nerves enter the hand.
You might want to try some inflammatories to see if you can remove some inflammation but you'll need to see a doctor to get this diagnosed.
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