I have a stiff neck, like a spasm or pinched nerve over my left shoulder. Eating causes a shooting pain down my neck. How can I alleviate the pain?

Esophagus. if it is related to swallowing a food, it can be very serious, like an esophageal diverticula, see a gastroenterologist.
NSAIDS / Heat. Recommend you try OTC NSAIDS such as ibuprofen for the pain and use a heating pad or a very hot bath to work to loosen the spasm. You may also ask someone to massage the area and stretch out the muscles involved which may offer some relief.