Loads and loads of us have been there - I understand that you feel like crap but your DD won't remember it, you know it wasn't a Good Thing and you'll move on. It will get better. Please don't beat yourself up about it - I hate smacking, but can't say I've never done it. I know I'm not alone in this, and nor are you.
Please don't feel bad. Many of us have BTDT. Its not the answer of course but give yourself a break - sounds like you have had a hell of a day. Calm yourself down and go and give DD a hug and have a real heart to heart about how sad you are both feeling and why.
I wrote a v similar post about a week ago. I felt dreadful and full of remorse. Follow Hassled's advice and put it down to experience and move on. What's done is done, and hopefully it will have confirmed that smacking is Not Your Style Of Parenting. Go and give her a huge hug.