Tension Headache: This is the most common type of headache and can be exacerbated by stress, leading to elevated blood pressure. The unilateral presentation (on one side of the head) is consistent with tension headaches, which can sometimes be localized to one area.

Migraine: Migraines are known for causing severe, unilateral headaches and can be associated with elevated blood pressure. They often have other symptoms like nausea, vomiting, and sensitivity to light and sound.
Hypertension-related Headache: Elevated blood pressure can cause headaches, typically described as a dull, throbbing sensation, often on both sides but can be unilateral. The timing of the blood pressure reading (5:40 a.m.) might suggest a morning surge in blood pressure, which is common in hypertensive patients.
Cluster Headache: Although less common, cluster headaches are extremely painful, occur on one side of the head, and can be accompanied by elevated blood pressure. They are known for their cyclical pattern and can wake patients from sleep.

Subarachnoid Hemorrhage: A sudden, severe headache (often described as "the worst headache of my life") with elevated blood pressure could indicate a subarachnoid hemorrhage, which is a life-threatening condition requiring immediate medical attention.
Hypertensive Emergency: Severely elevated blood pressure can lead to a hypertensive emergency, which may present with headache among other symptoms like chest pain or shortness of breath. This condition requires immediate treatment to prevent organ damage.
Temporal Arteritis: This condition, more common in older adults, can cause unilateral headaches and elevated blood pressure. It's crucial to diagnose and treat promptly to prevent complications like vision loss.

Pheochromocytoma: A rare tumor of the adrenal gland that can cause episodic hypertension, headaches, and other symptoms like palpitations and sweating.
Trigeminal Neuralgia: While not typically associated with elevated blood pressure, this condition causes intense pain on one side of the face and can be mistaken for a headache. It's less likely but should be considered in the differential diagnosis for unilateral facial pain.
Cervicogenic Headache: Originates from the cervical spine and can cause unilateral headaches. Although not directly related to elevated blood pressure, it's a possible cause of headache and should be considered, especially if there's a history of neck injury or strain.