If you get the antibiotic ointment (rather than drops), it helps to have the dog laying down so gravity will help pull the meds into the eye. We gave Star the eye meds while she was laying on her back/side. After she'd blink, I'd squeeze the meds near her eye. If it ended up on her fur/eyelashes, I would just hold her in that position. The gel will melt in a few minutes, and gets in the eye that way.
FYI, my kids have had pinkeye many time before, and have given it to me (one thing I wish they didn't share!). The drops sting like the dickens, the ointment doesn't hurt, so imagine how bad it would be if Zoey knew the drops hurt! And then, after Star had her eye infection, and my son got pinkeye, I gave him her meds and they worked like a charm (it was packaged for human use).
Good luck!