We, too, just dealt with...twice in about a 3 month time period. All three girls got it (5 1/2 yrs., 3 yrs., and 18 mos.) one after another. Unfortunately, my youngest had just weaned so I didn't get to try the breastmilk and I live in a small town where there was no eyebright to be found.
Pinkeye is very heat sensitive. The older ones can hold hot cottonball compresses over their eyes but with my little one, I just wiped out her eyes several times a day with very warm water. It took a good week plus for it to go away...more of a nusaince than anything.
Everyone told me to go to the doctor for "drops" but the problem is (as any basic health nut can tell you) they only work for bacterial infections...not viral. And most pinkeye cases are viral. If you go to the doctor, chances are they will give you the drops anyway...in case...just to cover all the bases. That's not the kind of doctoring I want to pay for.
Relax...and keep everyone's hands washed. Baby's primary caregiver might get the next case!