You should avoid exercises that obviously aggravate it--cause pain. This is a clear sign you are causing inflammation and maybe hindering the micro tears from healing. If you pulled a muscle, that's the best case scenario. Muscles are very vascular, meaning they have a great blood supply which leads to fast healing. Tearing or just slightly injuring a tendon is a less desirable diagnosis because a tendon is a thick, less vascular connective tissue that takes significantly longer to heal. This is what I would do:
1. continue with exercise that doesnt bother you. Follow it up by either ice or heat for about 30 minutes. Some say heat on sensitive parts that tend to "tense up" like the neck and back, but if you feel this is still a new injury with swelling present, if you can stand ice, I'd go with ice. It takes 20 minutes for the ice to penetrate deep enough for it to help, so suffer through it.
2. choose any waist up exercises carefully. do only exercises that you are certain you can do with complete control over your posture. for example: skip the shruggs for now. that's a repetitive exercise encouraging forward head, rounded shoulders, essentially poor posture. this will enflame the injury.
3. avoid combined movements. if you think of how your body moves you can isolate specific, simple movements. There is flexion/extension and rotation. Especially when you have an injury, you don't want to combine all these. This is a sure way people hurt their backs, and your neck is just a higher level of your spine.
I can't give advise on drugs because I don't know about that sort of thing, but I can give exercise advise based on years of training in therapy. Once you have recovered, you will want to start the shruggs and similar aggravating exercises at a lower intensity to see how you respond.