I'm glad you came through the car accident unscathed.
Although I am a very long way from introducing anyone to my children, I do, in a purely theoretical sense, think about it. I put in all sorts of considerations: we must be committed to each other for X months/years, we must be considering moving in together etc, but I know it will happen when it happens. It is probably like saying "I love you" for the first time. You think about it and think about it but when it happens, it probably just slips out by accident. I would try not to worry too much about it. If she were me, I would simply have said you are a friend, explained your car broke down nearby and it made sense for you to spend the night.
But I can see this weeks taken its toll on you. Maybe take some down time. Just chill out this weekend, put the D admin on hold, maybe catch up with some mates instead of dating. You know, take the pressure off yourself to be always doing 'stuff'.