According to Stanford Children's Health, the inside corner of the eye is called the lacrimal caruncle. This small pink nodule is made of modified oil and sweat glands, and it may become inflamed and itchy in response to allergies.
According to the US National Library of Medicine, the lacrimal gland is located to the side of the lacrimal caruncle. It continuously secretes tears to moisten, lubricate and protect the eye's surface. The lacrimal caruncle has two openings on both sides that suction the excessive moisture from the eyes as soon as the upper eye comes back up after an individual blink.