Maybe try breathing deeper and slower. More controlled. Even under heavy exercise you don't use your full lung capacity, so you can always get a little extra oxygen by breathing deeper.
It could however be your spine. When you run it sort of 'bounces' your skeletal structure, which can massage and soften certain tissues, to help correct alignment, but which can also pinch nerves if the spine is improperly aligned. Shoulder pain is a common sign of a bad back.
Start working on more core exercises, especially around your upper and lower back and see if that doesn't help to correct your shoulder. Keep running, but don't ignore that shoulder pain and push too had.