Should I feel awkward about this situation?

It's not weird at all. It may not be the generic situation in society, but that doesn't make it wrong or shameful in any way. As you said, you are just as loved and looked after by your dads than someone with a mum and a dad, so there's no problem. If people ask you about it, tell them, but don't let them tell you it's in any way strange or bad. If they find fault with it, they are just narrow-minded. :)