My left side of my elbow has a burning sensation, what could cause this?

Tennis elbow. If the "outside" part of the elbow is painful the most likely cause is a lateral epicondilytis or a tennis elbow.
?? nerve problem. Burning sensations in the body can be from irritated nerves. There are many nerves that run across the elbow and these could be irritated. Alternatively people with pinched nerves in the neck can have burning or other pains in the arm and hand. Best to see a doctor who knows how to diagnose these problems. Usually a neurologist or a physiatrist.