Adhesive Capsulitis (Frozen Shoulder): Given the history of shoulder dislocation, the pain in the shoulder and armpit, along with the sensation of numbness and tingling in the fingers, could be related to the development of adhesive capsulitis. This condition often follows trauma to the shoulder and can lead to reduced mobility and referred pain or sensations due to the complex innervation of the shoulder joint.

Brachial Plexus Injury: The brachial plexus is a network of nerves that come from the spinal cord and travel into the arm. These nerves control the muscles of the shoulder, elbow, wrist, and hand, as well as provide feeling in the arm. An injury to the brachial plexus could explain the numbness, tingling, and pain, especially considering the history of shoulder dislocation which could have stretched or damaged these nerves.
Thoracic Outlet Syndrome (TOS): This condition involves compression, injury, or irritation of the nerves and/or blood vessels (arteries and veins) in the thoracic outlet area, which lies between your collarbone (clavicle) and first rib. This could lead to pain in the shoulder and armpit, as well as numbness and tingling in the fingers.
Subluxation or Recurrent Dislocation: Given the patient's history of shoulder dislocation, it's possible that the shoulder is subluxed (partially dislocated) again or that there's an ongoing issue with instability, leading to the described symptoms.

Cervical Radiculopathy: Although less likely, it's crucial not to miss a cervical radiculopathy, which involves dysfunction of a nerve root in the cervical spine. This could cause pain, numbness, tingling, and weakness in the arm and hand. Given the potential for serious underlying conditions (like a herniated disc or spinal stenosis), missing this diagnosis could lead to delayed treatment and potentially permanent neurological damage.
Myocardial Infarction (Heart Attack): In some cases, myocardial infarction can present with referred pain to the arm, shoulder, or even jaw. Although the symptoms described don't classically suggest a heart attack, it's always critical to consider cardiac causes of chest or arm pain, especially in patients with risk factors for cardiovascular disease.

Pancoast Tumor: A rare type of lung cancer that grows in the upper part of the lung and can invade nearby tissues, including nerves of the brachial plexus, leading to shoulder and arm pain, as well as numbness and tingling in the fingers.
Neurogenic Tumors: Tumors that arise from the nerve tissues, such as schwannomas or neurofibromas, could compress or damage nerves, leading to the described symptoms. These are less common but should be considered in the differential diagnosis, especially if other causes are ruled out.