Don't be so hard on yourself. All parents have done something like that at one time or another. There are some parents that wouldn't have sacrificed like you did. They would have simply wrapped her in the coat. So actually it's a win. You care more about her safety and health than your own.
God damn it! I should have thought of wrapping her in the coat!
I think I mentioned to one of the other commenters... the funniest thing was that as I was stripping off in the toilet stall... I forgot to lock the door, and someone opened it with me naked from the waist up....