Well, generally speaking, you can get eye infection when you have a cold. As we know that if you get cold, your immune system can be weaker. And it will make your eyes become fragile. So at this time, it is easy for some bacteria invade into your eyes. so in that way, your eyes will be infected. Generally speaking, when your eyes get infection, it may lead to pink eyes or dry eyes. so just be careful when you have a cold. You should know that pink eye is redness and inflammation of the membranes covering the whites of the eyes and the membranes on the inner part of the eyelids. And it can be caused by irritation, allergies, eyestrain, and environment. And if your eyes are infected and get pink eyes, it can be dangerous for you. So anyway, you should take some medicine to heal your cold and strengthen your immune system. And also, drop some eye drops, so it can relieve the symptom. Also, taking the eye patch is also helpful.