Giant Cell Arteritis (GCA) with Arm Involvement: This is the most likely diagnosis given the context of the question. GCA can lead to arm pain due to inflammation of the arteries supplying the arm, such as the subclavian or axillary arteries.

Polymyalgia Rheumatica (PMR): Often associated with GCA, PMR can cause pain and stiffness in the shoulders and arms, which might be mistaken for arm pain directly related to GCA.
Thoracic Outlet Syndrome: Compression of the nerves or blood vessels that pass into the arm can cause pain, numbness, and tingling, which could be considered in the differential for arm pain.
Rotator Cuff Disease: Conditions affecting the rotator cuff, such as tendinitis or tears, can cause shoulder and arm pain.

Aortic Dissection: Although less common, aortic dissection is a life-threatening condition that can cause severe pain, often described as tearing, and can radiate to the arms. It's crucial to consider this diagnosis due to its high mortality rate if missed.
Acute Limb Ischemia: This condition, which can result from embolism or thrombosis, leads to a sudden decrease in limb perfusion and can cause severe arm pain, pallor, pulselessness, poikilothermia, paresthesias, and paralysis.
Myocardial Infarction: Arm pain can be a referred pain from myocardial infarction, especially if the pain is radiating down the arm.

Arteritis due to Other Causes (e.g., Takayasu Arteritis, ANCA-associated Vasculitis): These are less common forms of vasculitis that can affect the arteries supplying the arm and cause pain.
Neoplastic Conditions: Rarely, arm pain can be the presenting symptom of a neoplastic process, such as a tumor compressing nerves or blood vessels.
Infectious Arteritis: Infection of the arterial walls, which can be caused by bacteria, fungi, or other pathogens, is a rare but serious condition that could cause arm pain.