I finally decided to try something that I vaguely remembered hearing about, and if the guck-y yellowish green gunk didn't clear up right away I would make an appointment.
So I squirted a little breastmilk in the corner of the offending eye each time I fed her. By the end of the first day her eye looked much better. The second day it looked so good that I didn't "treat" her eye nearly as many times, but when we woke up the third morning it looked pretty bad again. We decided to a) start squirting more milk in it and b) call the doctor if it wasn't much better by the afternoon.
At each feeding that day I "treated" her eye. By the afternoon it was considerably clearer (and we decided not to call). After three more days I stopped the milk treatments and the gunk didn't come back. And that's just one way that breastmilk saved us a trip to the doctor's office (and maybe a course of antibiotic eye drops!)!