Cluster Headache: Characterized by severe, unilateral, stabbing or piercing pain, often described as occurring on one side of the head, typically around the eye. The duration of each headache can range from 15 minutes to 3 hours, which aligns with the provided duration.

Trigeminal Neuralgia: Involves sudden, severe, stabbing pain typically on one side of the face, which can be mistaken for a headache. The pain episodes are usually brief, lasting from a few seconds to a couple of minutes, but can occur in clusters that might fit the 15-minute timeframe.
Hemicrania Continua: A continuous, unilateral headache with episodes of more severe pain. While the continuous aspect doesn't perfectly match the 15-minute duration, the exacerbations can present with stabbing pain.
Short-Lasting Unilateral Neuralgiform Headache with Conjunctival Injection and Tearing (SUNCT) / Short-Lasting Unilateral Neuralgiform Headache with Autonomic Features (SUNA): These are characterized by brief, stabbing pains on one side of the head, often accompanied by autonomic symptoms like conjunctival injection and tearing. The pain episodes are very short, usually seconds to minutes, but can occur frequently.

Temporal Arteritis: Although the pain is typically more continuous and described as aching rather than stabbing, it's crucial to consider due to the risk of vision loss if not promptly treated. The headache is usually unilateral and can be severe.
Acute Angle-Closure Glaucoma: Presents with severe, unilateral eye pain, which can be perceived as a headache. It's associated with blurred vision, nausea, and vomiting, and is a medical emergency.
Thunderclap Headache: Characterized by a very severe headache that reaches its maximum intensity within a minute, often described as "the worst headache of my life." While the duration is typically longer than 15 minutes, the severity and potential for underlying conditions like subarachnoid hemorrhage make it a critical diagnosis not to miss.

Primary Thunderclap Headache: A rare condition where thunderclap headaches occur without any underlying cause. The pain is extremely severe and reaches its peak within minutes.
Idiopathic Stabbing Headache: Also known as "ice pick headaches" or "jabs and jolts syndrome," these are characterized by brief, stabbing pains, usually on one side of the head. They are typically not as severe as cluster headaches but can be quite distressing.
Cervicogenic Headache: Originates from the cervical spine and can present with unilateral pain, though the stabbing nature and short duration might be less common presentations.