Redness with a blood patch after a cut in the eye may be due to a small surface injury or bleeding under the eye surface. Chloramphenicol is an antibiotic and may be used if there is a risk of infection, but only as advised by a doctor. Avoid rubbing the eye and keep it clean to prevent further irritation. In most cases, the redness settles gradually with time. Consult a doctor if pain, vision changes, or swelling increase.