Aortic Dissection: This is considered the most likely diagnosis due to the sudden onset of sharp chest pain radiating to the back, which is a classic presentation for aortic dissection. The difference in blood pressure readings between the two arms further supports this diagnosis, as it suggests a possible disruption in the aortic flow.

Myocardial Infarction (MI): Although the pain pattern is not typical for MI, it cannot be ruled out, especially in a patient with hypertension. The sharp, sudden nature of the pain could be indicative of an MI, particularly if there are any associated ECG changes or elevated cardiac biomarkers.
Pulmonary Embolism (PE): Sudden onset of chest pain, although typically more pleuritic, could be a presentation of PE, especially if there are associated symptoms like shortness of breath or risk factors for thromboembolism.
Pneumothorax: Could present with sudden chest pain, but typically would have associated respiratory symptoms and findings on physical examination.

Esophageal Rupture: Although less common, esophageal rupture can present with severe, sudden chest pain radiating to the back and would be a catastrophic diagnosis if missed. It often follows a history of vomiting or an esophageal procedure.
Spontaneous Coronary Artery Dissection (SCAD): A rare cause of MI, but important to consider, especially in women with a history of hypertension. It presents similarly to a typical MI but has a different pathophysiology.

Acute Pericarditis: Could present with sharp chest pain, but typically the pain is more positional and relieved by leaning forward. It's less likely given the radiation to the back and the lack of mention of positional components.
Thoracic Aortic Aneurysm: While this could cause similar symptoms to aortic dissection, it's less likely to present with such acute onset unless it's rupturing, which would then align more closely with the symptoms of an aortic dissection.