What might be the cure of my recurring shoulder pain?

Various. Sounds like a chronic recurrent soft tissue injury like a tendinitis. It might be related to. Certain activity or repetative motion. Tendinitis usually hurts when you push on it. A single injection of cortisone might be curative.
Need diagnosis first. In medicine, it is important to make a diagnosis first before talking about a treatment or a cure. There are many causes of shoulder pain. I would advise seeing your doctor who will either make the diagnosis or send you to a specialist if they are not experienced in this area. Once the proper diagnosis is made, the right treatment and hopefully a cure will follow.
It depends. Could be a tendinitis, or something more serious like arthritis or a rotator cuff tear. See an orthopedic shoulder surgeon.
Many reasons. At your age, the most common cause of true shoulder pain is a rotator cuff issue. Either tendinitis or a small tear. It can also be a biceps tendon issue or even arthritis. Shoulder pain could also be referred from neck issues such as a pinched nerve. If it is chronic in nature, i would get it looked at.