Why dose my right shoulder close to my neck hurt when I breath in hard?

Muscle strain/spasm. As you inhale deeply, you expand your chest wall...And doing so, you move shoulder blades up and out, thus pulling on the muscles attaching to the upper and inner areas of the shoulder blade. If these muscles are strained somehow (common for people working on computer keyboards for long periods), they can be sore when you breath in deeply.. When in doubt, have it checked out.