Exertional headache: This is the most likely diagnosis, as it is a common condition characterized by headaches that occur during or after intense physical activity, such as running. The increased intrathoracic pressure and blood pressure during running can lead to headache.

Dehydration: Running can cause dehydration, especially if the individual does not drink enough water before, during, or after the activity. Dehydration is a common cause of headaches.
Tension headache: Running can lead to tension in the neck and scalp muscles, which can cause a tension headache.
Sinus headache: Running can cause sinus pressure and congestion, leading to a headache.

Subarachnoid hemorrhage: Although rare, a subarachnoid hemorrhage can cause a sudden, severe headache during physical activity, including running. It is essential to consider this diagnosis to avoid missing a potentially life-threatening condition.
Temporal arteritis: This condition can cause headaches, especially in older adults, and can be exacerbated by physical activity.
Pituitary apoplexy: A rare condition that can cause a sudden, severe headache, often accompanied by visual disturbances and other symptoms.

Cardiac cephalalgia: A rare condition where cardiac issues, such as coronary artery disease, cause headaches during physical activity.
Pharmacological headache: Certain medications, such as nitroglycerin, can cause headaches during physical activity.
Cervicogenic headache: A rare condition where headaches are caused by referred pain from the cervical spine, which can be exacerbated by running.