There's something about grad school rejections that really shake confidence. You pour your heart and soul into your applications, and then to think, "What's wrong with my application? What's wrong with me?" -- it's torturous. The thing is, grad programs often just aren't able to really give their candidates the time they deserve, and really amazing candidates -- much like yourself! -- get overlooked. What you need to do is shake your fist toward the sky, say "F you, Carnegie Mellon" and just remember how hard you worked on your applications. You sound like a really valuable asset to any team, and I am positive that more than one program would love to take you in. I bet your first rejection is also your last.
Best wishes!