I have been having neck and shoulder pain on my right side for a week now. at times the pain will go down my right arm as well. what would cause this?

Your neck: Thank you for the question. There are many potential causes, but among the most common is the irritation of a nerve in the neck. The term "cervical radiculopathy" refers to the pain that can run don the arm into the neck from a nerve irritation in the neck. Uusally a phyxical exam and appropraite imaging studies can diagnose the problem.

Pinched nerve.: It could be a pinched nerve in your neck. Shoulder problems usually don't refer pain beyond the elbow.