PINK EYE

So I took my son to the doctor this morning because his eyes were red, swollen and goopy, his red, itchy and puffiness started Saturday, the doctor said it wasn’t pink eye but gave him the pink eye antibiotic just because. I still just feel on edge about it actually being pink eye. I have 3 other kids and I’m really hoping they don’t get it. When does it show up in others after they’ve been exposed?