Why do the corners of my right eye hurt and itch?

Probably infected: Some people get an eye infection called blepharitis, which is an infection or colonization of bacteria based at the lid margins and corners. It creates inflammation, which leads to itching, redness of the lids, mild discharge or crusting esp. in the morning, and sometimes ocular irritation. Treatment is with prescription eye medication and warm compresses/cleaning. See an eye doctor for treatment.