Look at the links I pointed you to and get back to me. It's probably just rotator cuff tendonitis secondary to overactive deltoids, pecs, lats, etc...maybe a primary impingement.

The empty can test is simiilar to what your described you tried except the thumb is pointed down (like you are emptying a can) and the arm is held in the scapular plane...around 30 degrees in. This is a provocative test for the supraspinatus. There is also the "full can test" which is supposed to be just as good but the thumb isn't held all the way down but just to around 45 degrees. The idea is that this produces compression in the supraspinatus and and tells you its is weak, painful, etc...it's in the link.

Most likely you need to do the standard stuff and you'll be good. Stretch the internal rotators..pecs and lats, do scapular strengthening and stability, and implement rotator cuff strengthening. I would start with the scapular stuff and stretching first before putting in the RC stuff later on. This is just the basic beginning and you can get all the other details from the places I pointed you. Including some other specialized stretches and areas to work on.

Check range of motion in the shoulders with the tests and then correct any deficiencies there (it's easy really).

All this sounds really complicated but it's not. It's just sort of what you do to adress what can typically happen when you do a lot of heavy pressing, etc...and not just that.

You should basically find a lot of differences between the hurting shoulder and the non-hurting shoulder.