You may want to contact the Paul Chek Institute and see if he has an intern in your area.
I have battled shoulder problems for years. One thing I have learnt is if you have a reocuring injury there is usually a structural problem causing it,training is not the cause only the trigger.
It seems very likely that you have a rotator cuff disorder. I’m not sure if you’ve had any instabilities, dislocations, or bursitis, so that is a guess. If you participate in sports that may cause impingement syndrome (ie baseball pitching, swimming), you may want to lay off.
If you think its directly correlated to your weight training, you may want to make modifications. Test for impingement (horizontal adduction of arm, then force internal rotation) and supraspinatus weakness (use the drop arm test and empty can test). If these cause pain then a rotator cuff problem may exist.
I noticed you have pain while externally rotating. Rotator cuff problems are usually a combination of weak external rotators and tight internal rotators. Most do not stretch the internal rotators. We’ve all seen the guys who walk with their shoulders protracted so far forward that it looks like they’re in a posedown. Most also cannot perform a behind-the neck press without extreme discomfort. Tight IR prevent full ext rot and proper form.
Use a bent-arm pec stretch, st-arm pec strecth, pole/broomstick stretch, front delt/biceps stretch, and you may want to stretch the ext rot also. Find a good book on rot cuff rehab and these will be illustrated. You may also want to stay away from exercises that are potentially harmful to the shoulder. xtra wide grip benches, dips, dumbell pullovers (who the fuck invented these?), and upright rows. These encourage impingement (and sh pain).
Try the stretches and gradually move to the ext rot exercises. I would recommend seeing a PT who specializes in sports medicine or ATC. Like the other guy said, you may want to completely rest it(and ice)for a couple of weeks. Continued training will not help any joint laxity.
To perform a windmill grab a light set of dumbells and lie back like you’re going to do a set of dumbell flyes. Now go all the way down and from there go back all the way behind your head and from there come straight up back to the starting position. It’s just a good stretching exercise for the shoulders. Make sure you dont go heavy on these or you’ll end up hurting something.