A red patch in the corner of the eye where the white of the eye is, if it doesn’t hurt, itch, or affect your vision, consider subconjunctival hemorrhage to be a possibility. Subconjunctival hemorrhage is a rupture of a blood vessel in the conjunctiva, causing bleeding to accumulate in the subconjunctival tissue. It is mainly caused by the rupture of blood vessels in the conjunctiva due to rubbing the eyes, staying up all night, exertion, or drinking alcohol. Usually it does not affect vision or have serious consequences, and healing can be accelerated by the use of blood-absorbing medications. It can also be observed without any medication.