With these symptoms, we would suspect that your deltoid muscles are either strained or injured. Deltoids are the muscles covering your shoulders. It has three parts, the anterior detoids which cover your front shoulder, the middle deltoids which cover the side of the shoulder and the posterior deltoid which covers the back of your shoulders. Your pain can be mistaken as rotator cuff pain since they somehow connected to each other and there are some movements where in they synergize.
Now, the management approach depends on the extent of pain and how long this has been going. For conservative management of your shoulder we recommend these steps:
Ice for 3 to 5 days. Apply heat (hot water bottle, hot baths,. You may need to see a Physical therapist for some heating modalities.. From day 7 do light, pain free exercises (movements that do not cause pain) Cycling 2 to 3 times a week. Begin stretching (hold stretches for 30 secs, 5 times a day). From day 14 start to slowly get back into sports activities.
It is also important that you know if there is presence of tendinopathy and the only way to find out is to have some confirmatory tests. We recommend that you see a doctor to validate if the cause of pain is plainly muscle strain or tendinopathy.