Viral gastroenteritis or upper respiratory infection: At the age of 2, children are prone to frequent viral infections, which can cause headaches due to fever, dehydration, or sinus pressure. This is the most common cause of headache in this age group.

Ear infection (otitis media): Ear infections are common in young children and can cause headache due to referred pain from the ear.
Sinusitis: Although less common in very young children, sinusitis can occur and cause headache, especially if there's a history of recent upper respiratory infection.
Trauma: Given the age and curiosity of a 2-year-old, minor head trauma is a common occurrence and can lead to headache.
Allergies: Seasonal or environmental allergies can lead to sinus pressure and headache in children.

Meningitis: Although rare, meningitis is a life-threatening condition that requires immediate medical attention. Symptoms can include headache, fever, stiff neck, and irritability.
Encephalitis: Inflammation of the brain, usually due to viral infections, which can present with headache, fever, and altered mental status.
Brain tumor: Although rare in children, brain tumors can cause headaches, especially if they increase intracranial pressure.
Hydrocephalus: Accumulation of cerebrospinal fluid in the brain, which can cause increased intracranial pressure and headache.

Pseudotumor cerebri (Idiopathic Intracranial Hypertension): A condition characterized by increased intracranial pressure without a detectable cause, which can lead to headache and vision changes.
Arteriovenous malformation (AVM): A rare congenital condition where there's an abnormal connection between arteries and veins in the brain, which can cause headache and other neurological symptoms.
Subarachnoid hemorrhage: Bleeding into the space surrounding the brain, which is rare in children but can be due to trauma, vascular malformations, or other causes.
Intracranial hemorrhage: Bleeding within the brain tissue itself, which can be due to trauma, vascular anomalies, or other rare conditions.