While doing shrugs at the gym I injured my upper left back/shoulder/trap and have difficulty turning my head. Is this most likely just a pull?

Most likely. The muscles of the shoulder/back are big and powerful. An injury can cause significant immobility and discomfort. The mechanics of a "shrug" make this the most likely cause. Treatment might involve anti-inflammatory, muscle relaxants, massage, heat, gentle range of motion. An exam is warranted if it is not improving or it is worsening. In an extreme case, one would worry about the spine.
A pulled muscle- Yes. Your detailed description sounds like a muscle pull. If this is the case, the soreness and neck stiffness should subside within days with little more than rest, ice, and tylenol (acetaminophen) or an otc anti-inflammatory medication. If the symptoms do not resolve, then seek medical evaluation.