Yes, eye infections are common in newborns.
Babies do not have a strong immune system like adults and so, they easily catch infections. Catching cold makes your baby more prone to catch an eye infection. Viral eye infections are more common in babies. Exposure to allergens like household chemicals, dust, smoke and pollen, eye injuries and blocked tear ducts can also cause pink eye in babies.
If your baby gets eye infection often, you'd better take it to see the doctor immediately. The doctor can diagnose what kind of infection the baby get and give you proper suggestions.
It is not normal for newborn babies to get eye infection. Eye infection is most commonly due to bacteria and virtues infection, injury in eye and face. Sometimes pink eye and red eye are also causes of eye infection. Newborn babies cannot have a complete eye system. You may hardly to see eye discharges in the corner of a new baby who is 1-4 weeks old. However, if there are real eye infection on your baby, then go to see a doctor to take medical treatment in that it is possible that your baby suffered severe eye disorders. By the way, cold and fever may cause eye disorder for your baby, which just have a slight effect on your baby eyes.