Aww, I really feel for you. It's only been a few days though, and it will get better.
I managed for the first week and half eating soft foods and slimfast shakes! (I had all my top out and the rear at the bottom). It was a couple of weeks for me until it didn't hurt biting down on them. Take plenty of painkillers. If they are the front ones, can you cut food very small and eat on the back ones? I foudn chippy chips and fish very soft to eat and was a relief when I wanted a proper meal 
I dont think leaving them out too much while you are healing is recommended. As your gums might heal differently and they won't fit. Unfortunately my lowers didn't fit well at all, so I couldn't wear them, and so it's now 3-4 weeks I think and they don't fit at all!
How do yours fit? Mine felt very tight at first, but as I healed they got looser. And once it starting moving, it caused more pain, I had to start using a little polygrip, on the sides, away from where the extraction sockets are. Once it was stable, it hurt a lot less. You will get sore spots, but as your gums heal and change, it will get better.
I know what you mean about the embarrassment, too. I've had to do my best to joke and laugh it off. After years of grotty teeth I now have a hollywood smile to rival Simon Cowell, so no hiding it for me!! 
It is surprisingly common though, and people are sympathetic rather than judgemental.