I lived with similar symptoms to you and spent lots at an osteo thinking it was muscular/strength issue/frozen shoulder.
The pain continued so eventually (two years!!!) I went to doc and referred to physio – she did one thing and said I have to have a scan right away. Turns out I needed a subacromial decompression and was in and out within two weeks. My tendon had frayed a lot in that time but I gained full mobility in just 6 weeks.