How to Fix Shoulder Pain Pressing Movements?

There have been times during my training when I've experienced terrible shoulder pain while performing bench press or push-ups.

It's a weird pain you feel deep down in the front of the shoulder.

Almost like a stabbing pain.

It's not your chest or your triceps.

It's deep in the shoulder, slightly towards the front.

Have you felt it before?

What is it, and how do you fix it?