The sternocleidomastoid muscles are most likely those which are giving you problems. There are two of these muscles in the superficial layers of the anterior (front) portion of the neck that make the shape of a “V”, and they are primarily helpful in rotation, flexing and extension of the head. They run from the center of the sternum (breastbone) and the clavicle (collarbone) up to the mastoid process, a bone in the skull located behind the ears. These muscles tend to "bunch up" and become sore/painful when left in this state for a period of time, and "yes" it can occur on just one side. Press under the corner of your jaw (by your ear) to feel if it is unusually tender. If so, use a massage vibrator from behind the ear, to down under the jaw, working your way to where the clavicle meets the base of the neck next to the esophagus. I tend to see this in people that have stress build up or too much caffeine in their diet. You should see swelling (which is probably just the muscle in a contracted state) go down in a few days or sooner. If you have no resolution, then as always check with your doctor.
I suggest seeing your MD! it could be anything from a sprain or even your heart. So please see your doctor!