I have had a similar problem I went to therapy for, I'm also studying physical therapy myself. Could be an impingement created during those exercises, so many muscles originate and insert around the shoulder. I would give the area a little time to rest from those movements and recover first, since it sounds pretty irritated and you don't want it to become chronic.
Then re-check form on those two exercises (i.e. not having shoulder blades down and retracted during the press can cause an impingement). Do your stretches as long as they don't cause pain, and then maybe try some light band work to strengthen the area again.
Beyond that it may be a tear, or a problem deeper in the joint, but I would think the dips and overhead presses would cause pain as well if that were the case.
Just my thoughts...