Discharge from newborn’s eyes

My baby has been bringing out small clear discharge from both eyes at the year drop side every time my baby wakes up or when my baby crying. This has been going on for a few days now. What could be causing it please? My baby is 1 month old. If I squint some breast milk in there, is it safe for breast milk to be in baby’s eyes and won’t it get all over her eyes? Do I put the breast milk inside my baby’s eyes or around the outside of the eye? I tried squirting breast milk into her eyes... she was fidgeting and my breast was just touching her eyes instead