I have been working exclusively on my gymnastic skills ( back lever, handstand PU, pistol, and planche). My workouts include alot of dips, and pull-ups.
After reading the performance menu article on integrating gymnastic and weightlifting movements, I began integrating overhead presses and other weightlifting movements into my routine. I also read in Mark Rippetoe's Starting Strength that performing the bench press too much without enough overhead work to counter it leads to muscle imbalances, which can lead to soreness in the shoulders.
My point is that the bench press trains the anterior portion of the shoulders, much like the dips.
I train Mon,tues, thurs, and friday. Monday and thursday is when the planche, dips, or any anterior training of the shoulders take place. Tues and friday I include overhead work, such as a strict press or push-press. I have been following this training routine for 5 weeks now and have had little to no shoulder pain. I also do a lot of dislocates with pvc pipe both pre and post workout.
My suggestion would be to start including overhead work into your routine, maybe lay off of the dips for a week or so, and see if the pain goes away. Also if your not, work your shoulders through pvc dislocates. I do not know what your training style is or what goal you are working towards, but I hope this helps. As I know it works for myself.