Biceps tendonitis...from the brief description.
Is this where you feel it most...on the "X"?
If so, than its likely some inflammation of the proximal long head biceps tendon. This tendon runs over the head of the humerus and attaches to the scapula. Take a look:
Every time you externally rotate and abduct your humerus (raise your arm and do chest/shoulder work), that tendon is getting impinged (pinched) against the acromium process. This results in inflammation of the tendon. If it continues, the tendon will slowly weaken and can eventually rupture. Below is a bit of an extreme example (the bone spurs), but you can see how the position puts the shoulder in a dangerous state:
Without seeing you or your program, all I can do is make a guess based on past experience. My guess is a culmination of: poor technique on pressing exercises, excessive chest/shoudler work, inadequate mid-back and external rotator work, and some postural deviations at the shoulder girlde as a result.