are you breastfeeding? My aunty has a friend who used to be a nursing mothers consultant and she said you can use some expressed breast milk on a cotton square to clean bubs eyes as breast milk contains naturally occuring antibiotics, which is great because it is natural!
If you're breastfeeding, use your milk. It will clear it up really fast. Both my kids had it a lot when they were newborn and I used breast milk everytime, and it's great!
Probably better than drops from a chemist. It's got all the antibodies and other good stuff in it!