Viral conjunctivitis is common in children and does not require antibiotics either orally or topically.
Bacterial conjunctivitis is usually treated with antibiotic eye drops, but if a child is taking oral antibiotics anyway, that is usually sufficient (though a bit slower). Bacterial conjunctivitis that accompanies an ear infection is most commonly caused by H. flu — an organism that is sensitive to Augmentin.
If you elect to continue with the eye drops to speed the resolution, here is a tip:
Her eyes do not need to be open to put the drops in! I have children lie on their backs and close their eyes. I put a few drops in the corners nearest the nose. It will pool there until they blink. Then it slips in without that annoying ‘plunk’ of a falling drop hitting the eyeball.
When bacterial conjunctivitis is in only one eye, both eyes should still be treated so that it doesn’t ‘jump’ to the other eye. If the child is taking oral antibiotics, this counts as treating the other eye, so the drops can be placed only in the affected eye to make the treatment easier.