I would use the drops.

Liam had bad conjunctivitis and breast milk did nothing to fix it. He used to regularly get conjunctivitis and was on the drops or ointment quite often.

Something to note, (not to worry about though) is she might have a bit of a blocked tear duct as a lot of babies do, and might be a little susceptible to conjunctivitis, especially if she gets a cold. The blocked ducts do tend to resolve by around 12 months. This is what caused Liam's problems and now it is largely gone (he's 16 months).

Hope she recovers quickly!