Hypertensive Emergency: This is the most likely diagnosis given the combination of severe headache and hypertension. Hypertensive emergencies are characterized by severely elevated blood pressure with evidence of end-organ damage, which can include the brain, heart, kidneys, and eyes. A severe headache can be a symptom of hypertensive encephalopathy, a condition where high blood pressure leads to brain swelling.

Migraine: Although migraines can cause severe headaches, the presence of hypertension might suggest a different primary cause. However, migraines can sometimes be associated with blood pressure fluctuations.
Tension Headache: Tension headaches are common and can be severe, but they are typically not associated with significant hypertension.
Subarachnoid Hemorrhage (SAH): While SAH is a critical diagnosis to consider with sudden severe headache, it is not directly linked to hypertension as a cause, though hypertension can be a response to the hemorrhage.

Subarachnoid Hemorrhage (SAH): Despite being mentioned earlier, SAH is a "do not miss" diagnosis due to its high morbidity and mortality if not promptly treated. The sudden onset of a severe headache, often described as "the worst headache of my life," is a classic presentation.
Pheochromocytoma: A rare tumor of the adrenal gland that can cause episodic hypertension, headaches, sweating, and palpitations. Missing this diagnosis could lead to severe, uncontrolled hypertension and potentially life-threatening complications.
Reversible Cerebral Vasoconstriction Syndrome (RCVS): This condition can present with sudden, severe headaches (often described as "thunderclap") and is associated with reversible vasoconstriction of the cerebral arteries. It can be triggered by various factors, including certain medications and illicit drugs.
Posterior Reversible Encephalopathy Syndrome (PRES): Characterized by headache, confusion, seizures, and visual disturbances, PRES is associated with hypertension and can lead to significant morbidity if not recognized and treated promptly.

Cerebral Vasculitis: Inflammation of the blood vessels in the brain, which can cause a variety of symptoms including headache, and is associated with hypertension in some cases.
Primary Central Nervous System Vasculitis: A rare condition that affects the blood vessels of the brain and spinal cord, leading to symptoms such as headache, stroke, and encephalopathy.
Hypertensive Brainstem Encephalopathy: A rare condition where high blood pressure leads to brainstem dysfunction, presenting with symptoms like headache, nausea, vomiting, and altered mental status.