I have bell palsy, and the side that was affected by the illness feels like my veins are burning from the top of my shoulder, to my breast.

Facial nerve: Ruth, as the facial nerve is healing after Bell's palsy, the nerve might form new connections that don't behave normally. There is a muscle called the platysma in your neck and upper chest that is innervated by the facial nerve. Maybe this is sending false sensory signals through the nerve that feel painful. Ask your doctor if gabapentin or pregabalin might help you, if it's really painful.