Only a doctor can know this.
There are two types of pink eye: bacterial and viral. If her eye clears of redness soon, then likely it was a lash or she got a bit of soap in it. If her eye continues to stay red and is goopy, then she does need to see a doctor for anti-biotic drops. If it is viral pink eye, yes, they might give you drops, but she WILL be contagious until it abates. The drops do not do anything for viral pink eye other than to let working parents 'think' they are treating it. I believe they need to be home for at least 24 hours after starting treatment; you can call your child's school and ask about their exclusion policy; their student handbook should have it listed as well.
She cannot return to school with the red eyes until she has been treated. Period. It is, as you supposed, highly contagious. It's up to you to keep your hands off your face and eyes and do lots of your own handwashing. Be sure to launder linens which have contact with her face and head (Pillowcases).... when I was teaching preschool, I had to sanitize my entire preschool so that toys/materials wouldn't be contaminated.
And if her eye gets completely gooped up in the night, use a warm, very damp washcloth as a compress to break up the caked mucous on the eyelid. This happens from time to time and is very upsetting for children.