Thoracic Outlet Syndrome (TOS): The patient's symptoms of shoulder pain radiating to the neck and arm, along with tingling and the positive Adson test, strongly suggest TOS. The difference in blood pressure between the two arms further supports this diagnosis, indicating possible compression of the subclavian artery.

Cervical Radiculopathy: The radiation of pain to the neck and arm, along with tingling, could also be indicative of a cervical radiculopathy, especially if there is nerve root compression.
Glenohumeral Joint Disorder: The presence of glenohumeral tenderness on palpation suggests a possible issue with the shoulder joint itself, such as tendinitis or bursitis, which could contribute to the patient's pain.
Breast Pathology: Although less likely given the description, the mention of pain radiating to the left breast warrants consideration of breast pathology, including cysts or tumors.

Aortic Dissection: Although the chest X-ray is normal, the episode of syncope and the significant difference in blood pressure between the two arms necessitate consideration of aortic dissection, a life-threatening condition.
Subclavian Artery Stenosis or Thrombosis: The difference in blood pressure between the arms could also indicate stenosis or thrombosis of the subclavian artery, which is a serious condition requiring prompt diagnosis and treatment.
Pulmonary Embolism: The combination of dizziness, fatigue, and syncope could potentially indicate a pulmonary embolism, especially if there are underlying risk factors not mentioned.

Pancoast Tumor: A tumor located at the apex of the lung could cause shoulder pain radiating to the arm and neck, along with other neurological symptoms due to compression of nearby structures.
Arteriovenous Malformation (AVM): An AVM in the thoracic or cervical region could potentially cause the patient's symptoms, including the difference in blood pressure between the arms and neurological symptoms.