Hello,
It can be due to sprain,strain or tear of the muscles of the shoulder. Joint dislocations that are directly related to a trauma, such as in golf,soccer,tennis or other sports can also cause such kind of pain.Lastly,bursitis or arthritis of the joint can also be the causative factors.
I feel that physical examination by an orthopaedician is required to confirm a diagnosis. Till then,give rest to the right side.Apply some cold packs on the shoulder , back and chest and some analgesic(pain reliever)gel or cream.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
It could be nothing or something, but you'd be smart to go get checked.