Pink eye?

My 5 month old shows signs of pink eye (yellow discharge/crusting, red outside of the eye)... no red on the white part and doesn’t appear to be itchy. He also has a cold. I called the pediatrician’s office and the nurse said it does sound like pink eye and recommended we go to urgent care (they’re closed now).

I recently waited 2+ hours on a Saturday at urgent care.... I definitely don’t want to do that with a baby who could pick up more germs and is impossible to get to nap when we aren’t home. You can’t make appts on Saturdays, but I could make an appt for tomorrow morning.

Thoughts? Does it sound like pink eye or just symptoms of his cold? Is it super urgent or can we wait until tomorrow morning?

Other than being congested, he’s happy and has no fever or other symptoms.