I have a red vessel popping in my left eye corner. Do I add drops only?

Eye hemorrhage . Sounds like you have a bruise ( hemorrhage ) in the whites of your eyes ( conjunctiva) which appears tomato ketchup red and is usually due to rubbing the eye, forceful sneezing or coughing , &/or being on blood thinners. Generally not a sign of more serious problems like a bleeding or blood disorder. Eye drops for moisture if dry or for allergies if itchy are usually sufficient. Disappears ~ 2 wks.