Similar thing happened to me and the missus fella, we had a drop in heart rate of our little boy after a very long labour, then all of a sudden lot's of nurses and doctors everyhere, and the next thing, he was here (neville barnes delivery).
Happens so fast but at the time it last's a life time. I feel for you big time – brings back my experience like it was yesterday! The amount of relief you get once it's all over is euphoric eh?
Anyway big congratulations! Take her the biggest most prettiest flowers you can buy tomorrow and a card with a heartfelt message inside, she probably won't appreciate them much at the time, but once she's better – trust me on this one, she'll remember your attempt at being the perfect new daddy! 😉
Good luck with all – kids are the best fookin thing EVER!!!