1. The pedi is right. Kids in daycare get sick. First children get sick a lot. (Second children get sick, too, but who the hell has time to notice? Just kidding.) Most kids I know have an on-and-off runny nose from about Thanksgiving through Pesach. When it's clear, it's a cold starting. When it's yellow, it's a cold ending. Or an ear infection. Or a sinus infection. Or something. Then it's clear again: the next cold starting up.

OTOH...kids who have been in daycare are, statistically, out less often from kindergarten through (iirc) 4th grade. There was a study, but damned if I remember where I saw it.

2. You're in a neighborhood full of experienced mommies (and daddies). Most of whom are themselves little (or big) petri dishes, but whatever. You get like this, pick up the phone, say "hey, Ben's sick, I need a break, can I pop by and let him scream at you for a while?" The crying isn't as bothersome when it isn't your kid, and then you don't have to feel guilty at taking a break because frankly he's too young to care that the warm body holding him isn't you.