Make sure you apply good hygiene around the eyes and whatever you use in cleaning off the discharges(pus). Clean each eye separately and discard the wipe or soft cloth. You should try and see a nearby Optometrist(eye doctor) to examine your baby's eyes n ask further questions n diagnose properly. But I'd suspect Bacterial Conjunctivitis here and it should be clear after a few days except if there is reinfection. Your baby will be fine.

Bacterial conjunctivitis most likely! Kindly see a doctor for proper evaluation and treatment'