Adhesive Capsulitis (Frozen Shoulder): This condition is characterized by pain and stiffness in the shoulder joint, making it difficult to move the shoulder, including putting the hand behind the back. The pain and limited mobility are key features that align with the symptoms described.

Rotator Cuff Tendinitis: Inflammation of the tendons surrounding the shoulder joint can cause pain, especially when moving the arm in certain positions, such as behind the back.
Subacromial Bursitis: Inflammation of the bursa that cushions the rotator cuff tendons can cause pain when moving the arm, including when putting the hand behind the back.
Shoulder Impingement Syndrome: This condition, where the shoulder blade puts pressure on the underlying tissues when the arm is lifted, can cause pain and limited mobility.

Thoracic Outlet Syndrome: Although less common, this condition involves compression of the nerves and/or blood vessels that pass into the thoracic outlet (the space between your collarbone and first rib), which can cause pain in the shoulder and arm, especially when the arm is raised or put behind the back.
Cervical Radiculopathy: Nerve root compression in the cervical spine can cause pain that radiates to the shoulder and arm, potentially worsening with certain movements.
Myocardial Infarction (Heart Attack): In rare cases, shoulder pain can be a referred pain from a heart attack, especially if the pain is accompanied by other symptoms like chest pain, shortness of breath, or nausea.

Pancoast Tumor: A rare type of lung cancer located at the top of the lung that can cause shoulder pain due to local invasion of the tumor into the brachial plexus or ribs.
Polymyalgia Rheumatica: An inflammatory condition that causes muscle pain and stiffness, particularly in the shoulders, which could potentially cause difficulty moving the arm.
Osteonecrosis of the Humeral Head: A condition where the blood supply to the bone tissue at the head of the humerus is interrupted, leading to bone death and potentially causing shoulder pain.