Get the shoulder issue fixed first. Get it scanned and checked out by a professional. Looking at the selection of exercises that could make any shoulder choke up- as mentioned above fixing the issue and training for those goals can be difficult. There is some good reading material by Eric Cressey, Bill Hartman and Robertson etc..
But looking at your routine there is a hell of allot of horizontal pushing. Hows your pull to push ratio? Are you balancing them out? Doing that is just going to make the pecs tighter and add to the problem. Not only that how is your over all mobility and flexibility? Do you get soft tissue work done- if not go see a good physio?
As mentioned before are you one of those people who live by the bench?
How much scapular stability work do you do?
There is so many things to mention which is way out of the scope of one post.
Ive been trying to fix my shoulder its getting better but i wanted to get it it fixed by a professional. Id recommend the same and trust me finding a good physio is much trickier than it sounds.
You can try really attacking all over body mobility and flexibility- attacking the upper back and scapular/ lower trap function, fixing your core strength, learning how to perform a productive warm up to relieve your problems and fixing your posture. Then learning how to lift and going on a 5x5 type of program, thats what i've done and my shoulder isn't hurting too bad but i don't bench- don't need it because of the type of sport i participate in.
As for nutritional help glucosamine and allot of high potency fish oil could help down the line.
Hope my 2 cents helps
