Migraine with Aura: The patient's symptoms of visual aura followed by a moderate to severe headache, nausea, and vomiting are classic for migraine with aura. The headache being unilateral and more intense on one side, in this case, the right side above the eye, also supports this diagnosis. The pattern of episodes, including the resolution of headache after vomiting, is consistent with migraine.

Tension-type Headache: Although less likely given the presence of aura and severe headache, tension-type headaches can be bilateral and frontal. However, they are typically less severe and not accompanied by nausea or vomiting.
Cluster Headache: Given the severe, unilateral nature of the headache and its location around the eye, cluster headache is a consideration. However, cluster headaches are typically shorter in duration, occur in clusters or cycles, and are often accompanied by other autonomic symptoms like nasal congestion or eye watering.
Chronic Daily Headache: If the patient's headaches become more frequent, this could be a consideration, but given the current episodic nature, it's less likely.

Subarachnoid Hemorrhage: Although extremely unlikely in a 13-year-old without trauma, any severe headache, especially if described as "the worst headache of my life," warrants consideration of subarachnoid hemorrhage due to its potentially fatal outcome.
Idiopathic Intracranial Hypertension (IIH): Also known as pseudotumor cerebri, this condition can cause severe headaches, often worse in the morning and improved by vomiting. It's more common in obese females and can lead to vision loss if not treated.
Brain Tumor: Any new onset of headaches, especially if accompanied by other neurological symptoms, should prompt consideration of a brain tumor, although this is rare in the context provided.

Trigeminal Neuralgia: Characterized by sudden, severe, shock-like pain around the eyes, lips, or nose, typically on one side of the face. It's rare in adolescents and doesn't usually present with the headache pattern described.
Hemicrania Continua: A rare headache disorder characterized by a continuous, often unilateral headache with periods of exacerbation. It's less likely given the episodic nature of the patient's symptoms.
Cervicogenic Headache: Refers to headaches caused by cervical spine (neck) disorders. While possible, the description provided doesn't strongly suggest a cervicogenic origin.