I damaged the roator cuff on both shoulders and having visited 4 doctors and spent time with 5 PT people I finally read a newspaper article that explained the nature of the injury. We are like apes and not built for heavy lifting with our upper body. Very little relative strength when a weight or work task has our hands higher than our shoulders.
I was fortunate in that with the second damaged rotator cuff I was treated by a PT who was a former trainer with the Giants pitching staff. He explained that when the pain of the injury causes people to not lift their arm as high that in a matter of weeks the tendons will shorten and then surgery is required. He stretched my arm to get my range of motion back and he went a great deal further than I could have done by myself. Heat and massage and then stretching and then 15-20 minutes with an ice pack. After 4 weeks and 12 sessions my range of motion was back to what it was before the injury and after that I am much more careful about doing overhead work.
It is easy to have shoulder pain from stressing the trapezius muscles with riding and a good approach is to do exercises with lightweigh dumbbells to strengthen these muscles. Planks are good for torso muscles but not that great for the shoulder muscles.