I know exactly how you feel. Exactly. Typing this brings it all back.
When my daughter was 3 we were on the dock in the spring. My dock is 32 feet long and I was unhooking a trout near shore on the dock and my wife was sitting on the couch near shore. My daughter was at the end of the dock and fell in. My wife screamed and all I could tell was that my daughter was gone...just a splash then nothing. From the dock you could not see her at all (top of dock is about 1 foot above water). I just ran and blindly jumped off the end - I started to see my daughter in the water as I flew through the air - face an inch under the water, bubbles coming out of her nose, eyes-wide open looking up with her white ball gown flowing in the water.
She still claims she saw a starfish down there.
I don't know if she would have floated/swam for a bit or not. I do know that this was the scariest thing to happen to me as a Dad.
I was on the same dock as her and this was still a very close call. Lesson learned and I hope everyone reading this learns to stay close when the children are young. These incidents are accidents - and you need to be prepared.
My daughter has since taken swimming lessons twice a year. She's five now and is a much safer swimmer now, but I still stay within a half-dock of her now.
Very glad that your incident turned-out well Greg. Stay close to the little ones and enjoy every minute with them.