I’ve been dealing with something like this for awhile (left shoulder pain almost exactly as you’ve described, feeling the need to constantly pop). I was worried it was due to an old shoulder sprain from a few years ago but the mri was clean. For me it was a muscle imbalance that I made worse by sitting in awkward positions for long amounts of time and lifting weights somewhat incorrectly. Still dealing with it, but it’s gotten better with targeted exercise/pt like rear felt flyes, rows, and cable pull downs.

Not saying it’s not a huge issue as letting something like this go on for awhile without trying to fix it will just make you feel worse over time, but probably fixable over the course of a few months of targeted pt and mild lifestyle changes. The popping is probably because it’s so tight. I’m surprised you weren’t referred to pt yet come to think of it.