MJ had a similar problem.
Although it wasnt infection i used calendula tea when i cleaned her eyes and it went away really quickly.
I dont know if it will work for you, but helped.
If you are interested...
I bought calendula flower tea from a health food shop, brewed the tea, added cool water to cool it and when it was the right temp i would clean both eyes out. Did it after every sleep.

We she got a teething rash or sore bottom i would also add the tea to her bath water and it would clear it right up.
I also used it as a bum wiping solution with home made wipes and we never got Nappy rash - other than when she had gastro...

Hope this helps, if not with you, but might be useful to someone else.
I hope your DD's eyes right themselves soon
xo