Whenever I reach overhead with my right arm, the shoulder on that side automatically lifts up as if I'm shrugging. This doesn't happen on the left. What could be causing this to happen?

There may be a muscle imbalance. Too much activation of the upper trapezius muscle may be the problem. The trapezius is a large muscle in three parts. The upper part is across the top of the shoulders and contracts to shrug the shoulders.

Most muscles work in coordination or in opposition with others. They either work together at the same time or one contracts while the other is relaxed. To keep the shoulder from rising up when using the arm overhead, the upper trapezius and the serratus anterior muscle (SA) work together. The SA is attached to the scapula (shoulder blade) and at the other end to the upper eight or nine ribs.

You can have this tested by a physical therapist. The therapist will be able to give you some exercises to bring these muscles under better and more normal control.