Tone, a lot of good info is in this thread. Speaking from a host of shoulder injuries myself, and my academic background, I will agree with most everything said in this thread. Since most of the posts here were really good, I’m pretty much just repeating what they said:
The pain and tightness is likely from a muscular imbalance, and could be a small accumulation of inflammation. The popping sound is likely a bit of instability as Bushy said, but doesn’t necessarily mean the joint is lax, but could be due to the imbalance as well. It is very likely a combination of the two–something is tight and something is loose, probably from overuse of something.
I would suggest doing all of the above stretches–broomstick up and over the shoulders (I actually use a non-stretchy band of fabric, basically a nylon strap, as it allows more freedom of wrist motion, and is better for portability), the joint capsule stretch on the website, and actually the same type of stretch but in other planes of movement, and of course general pec/lat/tri stretches. In fact I’ve had multiple athletes tell me they either can’t press as much weight or can’t press at all pain free without doing the should shoulder up and over stretch (broomstick).
the other thing you need to do is stabilize the joint a bit more. Do internal and external rotation movements using DBs and/or bands. The YTWL exercise is also good. You likely need to focus on the external rotation movements for the time being, though perhaps not. If by doing too many external rotational movements you experience pain, balance it out with more internal rotation movements. You may need to improve overall joint stability, and not just external rotational stability. Basically, if what you start with works, keep doing it, if not, try something else, but don’t stop doing something.
It sounds stupid, but make sure you’re hips and back extensors are flexible enough as to not impede movement. Abdominal strength and general core stability can also work wonders, as the whole body is connected. This part of my advice won’t 100% help your problem, but it will make a small contribution to overall function to have lower body and core flexibility/stability.
The 2:1 or 3:1 pull:push is a good idea, at least until the pain from pushing goes away. When that happens resume normal loading, and don’t try to go overboard with the pushing to compensate for the time off. I think a bit better advice than this is to make sure you’re balancing internal and external rotation, as some benching and pulldown movements can be either internal or external depending on how you do the exercise. I would suggest doing more rowing exercises than pulldowns for the back, at least 2:1. Similarly, ditch the BB for pressing movements, at least 2:1 DB:BB. This isn’t necessarily an ongoing necessity, but it certainly would be good until your shoulder gets better.
After the pain goes away don’t stop doing these things. Pain is not a reliable indicator of injury recovery, as the remodeling process takes some time to complete after the pain dissipates. Once you are healed up and pain free, you can lower the volume of stretching and strengthening exercises to maintenance levels, but I assure you if you have a chronic injury and you stop doing them completely, the injury will come back at some point.
Good luck.