Well, generally speaking, it is possible to have bloodshot eyes after you have taken the eye surgery. As we know that after the surgery, your eyes will be sensitive and fragile, it is easy for your eyes to be infected by bacteria and allergies. When your eyes are infected by allergies, and it will lead to pink eyes, turn to red and bloodshot. For your situation, you can wear the eye patch to protect your eyes. Also, after the surgery, you should eat foods high in beta-carotene, Vitamin C and Vitamin E, such as garlic, onions, beans, vegetables, celery, seaweed, apples, carrots, tomatoes, turnips and oranges. Anyway, you should be careful about it.