Tension Headache or Migraine: These are common conditions that can be triggered or exacerbated by vomiting, possibly due to dehydration or the physical act of vomiting itself. The intense headache could be a migraine, which is often accompanied by nausea and vomiting.

Dehydration Headache: Vomiting can lead to dehydration, which in turn can cause or worsen headaches due to the reduction in fluid volume and potential electrolyte imbalances.
Gastrointestinal Issues: Conditions like gastroesophageal reflux disease (GERD), gastritis, or gastrointestinal infections could lead to vomiting, which then triggers or worsens a headache.
Medication Overuse Headache: If the patient is taking medications for headaches and is vomiting, this could lead to a rebound effect, causing more headaches.

Subarachnoid Hemorrhage: Although less likely, a sudden, severe headache (often described as "the worst headache of my life") accompanied by vomiting could be indicative of a subarachnoid hemorrhage, which is a life-threatening condition requiring immediate medical attention.
Meningitis: Infection of the meninges can cause severe headache, fever, and vomiting. It's crucial to consider this diagnosis, especially if the patient has other symptoms like fever, stiff neck, or altered mental status.
Increased Intracranial Pressure: Conditions that increase pressure inside the skull, such as a tumor or idiopathic intracranial hypertension, can cause headaches that worsen with vomiting due to increased pressure.

Chiari Malformation: A structural defect in the cerebellum that controls balance can cause headaches, especially after vomiting, due to increased intracranial pressure.
Pseudotumor Cerebri: A condition characterized by increased intracranial pressure without a detectable cause, which can lead to headaches that might be exacerbated by vomiting.
Cyclic Vomiting Syndrome: A rare condition characterized by recurring episodes of severe vomiting, which can be accompanied by headaches, possibly due to dehydration or the syndrome itself.