Eye medicines come in two forms—ointment and drops. Drops are easier to give but can sting a bit if the eyes are inflamed. Ointment requires more control and less squirming because you have to get close to the eye.
Holding baby still requires two people (or one person can “mummy” the baby in the burrito wrap) to keep baby’s hands from getting in the way. If an extra pair of hands is available, have that person hold baby’s head while you hold baby’s body so you don’t have a moving target—this gets harder as baby gets older. Newborns are easy enough to handle solo. Put baby on a soft surface— couch, bed, and carpet—where you can bend over her.
Hold the medicine in your dominant hand and pull down the lower eyelid to form a pouch into which you deliver the drops or a ribbon of ointment.