Hot Fomentation. Gentle Shoulder Stretching. Core Strengthening Exercises. Gentle Neck Exercises. Avoid sleeping on affected side.. Warm up and cool down is a must.

Has the pain occurred after an injury or a fall on your shoulder?? As you work involves working for long duration on your computer the problem could possibly due to work related musculoskeletal injuries or repititive strain injuries. Usually the right hand uses the mouse and is more often mobile than the left hand during a computer operation, the right hand muscles usually suffers the microtrauma from the wear and tear, inappropriate rest periods. This accumulates over time and the pain becomes almost constant. This also causes the other muscles of your shoulder and scapula to get overworked leading to muscle dysfunction. Which further aggravates the problem. The snapping occuring in your shoulder might be due to ligament snapping, but other possiblities should be ruled out.

Agree with Dr Patil. You need regular physio.