You are not alone. I had to force back tears as my younger daughter ran off eagerly ahead of her teacher at her first day at school.
Move on a good few years to the Ladies loos at Durham Uni. as I prepared to leave my elder daughter there as she began her course. It was hard to get in because of sobbing mums, to try to patch-up make-up was all but impossible because everyone was trying to get in front of the mirror bent on the same repair job.
My eyes kept leaking all the way down the A1 until we got home.
Both mine were fine, yours will be, but it's a huge wrench. My then OH couldn't understand either.