What might lead to neck pain left side of neck?

Muscle spasm: Tight contracted muscles can cause pain like that. Try otc analgesics (ibuprofen, aleve) plus heat and gentle stretching.

Multiple causes: Without knowing your history, it is difficult to give you a direct answer. Usually neck pain is caused by irritation of a spinal structure-e.g.-disc, facet joint, nerves. These in turn lead to muscle spasms. Other structures that reside in the neck may also be responsible for the pain-esophogeal inflammation , carotid artery dissection, myocardial infarction, etc. Bottom line, see your doctor.