So sorry to hear about
your first accident and try not to feel embarrassed or ashamed; it's not your fault.
I've had to poop many places and sometimes I just couldn't hold it. Outside an airport (while I was working). On my way to a friend's house during an emergency stop at a Chick-fil-a. Staying late at school waiting to get picked up. Oh yeah, and twice recently (within the past two weeks) I had to dispose of two pairs of pants and boxers.
I picked up some Depends while I was on vacation a short while ago for added peace of mind although I never really trusted their ability to soak up any volume. I was finding though that most urgency poops were low volume blood/mucus mixtures as opposed to full blown explosive diarrhea.
Just know that there are a lot of us out there that have been through and survived these moments as well. Hopefully that provides you some relief/comfort
-R