Seems like batteries in Iphone 5 has this problem. I got the same experience with screen bulging out in upper right corner and so it is a open glitch between the screen and the phone. But from what I understood this is no guarantee case for Apple. Made me wonder about customer support. Used Apple products for 22 years and are found about them, but the world has changed outside the Apple universe.
Next replacement of my phone will be in December. Use it with scotch tape to cover the glitch in the meantime. Not sure if it will be an Apple product next time.