You’ll need a medical examination to find out what soft tissue structures might have been injured. With the mechanism of injury you describe, it sounds like a possible rotator cuff injury. The rotator cuff is a group of four tendons and the muscles that envelope the shoulder and hold it in place.
Along with stabilizing the shoulder joint in the socket, each one of the tendons has a specific job. Placing your hand behind your back requires medial (internal) rotation of the shoulder. The primary muscle for that movement is the subscapularis.
Subscapularis injuries occur when the shoulder is suddenly laterally (externally) rotated or hyperextended with force. The arm is next to the body at the time of the injury. With an injury to the subscapularis, there is weakness in internal rotation and excessive shoulder external rotation.
An orthopedic surgeon will test each muscle of the rotator cuff to determine what might be wrong. Usually the history and clinical tests are enough to make a diagnosis. X-rays can rule out fractures. An MRI or a CT scan may be ordered, especially if the surgeon is considering surgery as a possible treatment option.
Studies show that early diagnosis and treatment yield the best results. Don’t wait too long before you have someone look at this and at least give you a diagnosis. It’s possible with time and a rehab program, healing and recovery will occur without surgical intervention. But getting started while the body is in a reparative stage is important.