When I was a child, if you had pink eye, your mom took a warm washcloth and gently cleaned your eye now and then, and unless it was really bad you went to school. It got better in a day or two by itself, but it hurt unless you kept your eyes closed, and then they'd be glued together and you had to put the warm cloth on again. Unless he has some super nasty strain of pinkeye, it's likely that it'll clear up on its own in a couple of days even without drops. If you get the drops on the outside of his eyes while they're closed and can get him to blink, some will get in the eye. The drops do make it feel better, but I remember having drops put in my eye as a child and it was very scary, seeing a big dropper thing come looming up in front of my eye while my mom tried to hold my eye open. Try just putting the bottle in your fist so all he can see is your hand, don't touch his eye at all, and see if you can smooth the hair off his forehead and get some drops in the inside corner of his eye, where he'll blink them in. And try laying a warm, damp cloth on his eyes, which is soothing.