The bottom left side of my neck and the top of my shoulder hurts when I swallow and it doesn't ease it by turning my head or massaging it. What is it?

Esophogus? Your description that it hurts when you swallow is concerning for something that is near your esophogus (swallowing tube) or something that involves your esophogus. I would recommend you see your doctor for an evaluation.
See a doctor. More dtailed hisrory and examination is needed . I recommend that you see a GI specialist for an esophagoscopy , if no explanation he/she may direct you to a neurologist.