Yup. I tore a muscle while lifting at the gym a while ago. Persevered for months with a niggle, ended up seeing a colleague shoulder specialist. He operated in march, lots on inflammation, but it's improving. Recovery can take 12months post op. Funny how we often assume "it will settle down" but occasionally it doesn't.
If your GP has had a look, you're probably on the right track, a good physio can perform mobility checks & get a good idea of which parts are affected. Shoulders are amazingly complex.