can babies have pink eye?

my 2.5 month old daughter has been having more eye boogers in one eye than normal the past few days but when I got up with her just now to change her diaper her eye was all crusty and a little stuck shut on the outside. like her lashes had gotten so wet they crusted shut when it dried. I opened her eye and while it's not red it just seems like pink eye to me. but I don't know if babies can even have pink eye. she hasn't come in contact with anyone that has it. probably gonna bring her to the urgent care today? or should I just make an appointment for tomorrow with her pediatrician?

*she is NOT in daycare of any kind so I know for sure she's not been in contact with anyone that is it.