What causes burning sensation in the left arm ?

It is most likely coming from a nerve. It all depends on the location ie entire arm could be pinched nerve in neck or if in wrist could be the median nerve (the one that goes under carpal tunnel) . It would be unusual to have one sided with vitamin deficiencies or systemic diseases. If you injured area can cause that too. Hope this helps.

The burning of the arm is most likely an inflamed nerve. It can be from the neck, shoulder, elbow, wrist. Vitamin b12 deficiency classically causes symptoms in both feet and or hands, but in my experience also predisposes and /or contributes to the one-sided arm symptoms. See a doctor

Most likely secondary to neuropathy, which could well be a proximal problem in the shoulder girdle involving the brachial plexus, such as Parsonage-Turner Syndrome, or even Thoracic Outlet Syndrome. Other locations could be considered. A neurological consultation could be useful, and an EMG test could be confirmatory.