You may be describing a problem called shoulder impingement. Impingement of a tendon causes pain for swimmers at the point of hand entry into the water. In this position, the arm is rotated inward with the hand turned palm and thumb down. The supraspinatus tendon of the shoulder rotator cuff may be getting pushed up against a ligament that crosses the tendon just above it.
Before starting any kind of exercise program, it is important to find out exactly what is causing your symptoms. There are a variety of specific tests that can be done by an orthopedic doctor. Early identification of the problem can help prevent small problems from getting worse. Treatment may involve anti-inflammatory medication, physical therapy, or surgery.