I have this sharp throbbing neck pain on the back of my neck, left side by my spine every time i move my head from side to side. occured during stress?

Muscle spasm: Most likely this represents muscle spasm, very common in people under a lot of stress, or who keep the neck in a fixed position too long, or who have structural spinal problems. This can be relieved by daily stretches, avoid prolong or awkward neck postures and learning to reduce stress.

See Doctor: First try nsaids like ibuprofen, aleve and you can even add some tylenol (acetaminophen) to help with pain. Ice the area for 20 min at a time and see if these help reduce the pain. If this persists longer than a few days, consider seeing your doctor for stronger medications to help. Typically most people get better within a few weeks of an injury. If not better consider further imaging studies to evaluate.