The baby probably has a blocked tear duct. You need to massage the area below the tear duct and towards the nose. The tear duct is clogged and they can get infected. You will probably be given a prescription for an eye ointment, since baby's are too little to use drops on. The infection will take a while to clear up, and it probably will re-occur down the line, so save any left-over ointment. I was told by my doctor to clean the pus off with sterile room temperature water (boil it for 5 minutes) and a cotton ball. Dry the area well, as any left over water can lead to re-infection since it will breed bacteria. My DS had this problem, and he had a re-current eye infections from this until he was 8 months old, when the tear duct finally opened. Doesn't your practice have after-hours emergency coverage? I'd just call them and have a doctor paged, so he/she can call in the prescription for the eye ointment. No reason to have to take a young infant to an "express care" place with all the germs.