What does a burning, tingling feeling in your left arm mean?

Likely pinched nerve. You have not specified precise location in the arm. Your symptoms suggest pinching of nerve or nerves in any of following locations; neck, shoulder area behind collar bone, elbow or wrist depending on exact location of your symptoms.
See a doc. Left arm numbness can be from a herniated disk in the neck or nerve compression in the upper extremity. Less likley other etiologies include cardiac and abdominal causes. See an orthopedist.