When treating run of the mill bacterial conjunctivitis, I was taught to use erythromycin ointment for young infants that are not yet walking, and polytrim drops for older kids. The ointment is nice in that it sticks in the eyes better, but it can be annoying to have goopy eyes for an ambulatory toddler. This is a nice summary table. Gentamicin and sulfas in particular can often cause eye irritation, so are not a great first choice for routine pediatric non-contact lens conjunctivitis. Also, it can be hard to differentiate viral from bacterial conjunctivitis, and in the spirit of “first do no harm,” you don’t want to worsen the symptoms of a viral conjunctivitis that was going to self-resolve anyways.