After your newborn is born, you may notice that she has puffy eyes. This is pretty typical from the labor and birth. Pressure on the baby's face causes some swelling that goes down fairly quickly. Some newborn babies may actually have small broken blood vessels in the whites of their eyes, also from birth. This goes away as well.
Most babies will have antibiotic ointment put in their eyes close to the time of birth. This can leave a gel like substance on their eyes. This is done to prevent infections in the baby's eyes.
Obstetrics: Normal and Problem Pregnancies. Gabbe, S, Niebyl, J, Simpson, JL. Fifth Edition.