Okay, I don't really know the whole situation from the very very beginning, but from what I've read, you should probably end things with him and not want him back. Just move on with your life because guys like these are nothing but trouble.
So this ex of yours, he broke up with you and then the next day you got back together, right? I can see how that could be embarrassing for other people to know ("What? You guys just broke up yesterday! What the heck?"), but people would have eventually found out anyway. I can also see how it's awkward that other people found out about this earlier than you two had hoped, but if he truly liked you and cared about you, he wouldn't have broken up with you again just because of that. I mean seriously, what type of decent person would do that?! People finding out early isn't such a big deal in the whole scheme of relationships. Yes it can be a little bit awkward at first, but people get over that fairly quickly. And if he was serious about the relationship, something so small wouldn't have stood in the way.
And that is proof to why you're better off without him. If he's not in this relationship as committed as you are, then why bother wasting your time and energy for it? It wasn't going to end well and you would've probably regretted a few things. That's why consider it quite fortunate that you were left off the hook fairly early on before anything deep started to develop and your heart gets broken again. I mean if he really passed up the second chance to be with you for something so stupid and not important, then he needs to get his priorities straight and you need to move on. You deserve someone better.
I know that this is all fairly hard to process at first, but it is for the best. Just think about it. I hope this helps and good luck to you.