Gray lines/grid on iPhone 5 screen?

A couple of weeks ago, I posted on here about a problem I was having with my lock screen: https://discussions.apple.com/thread/5456143?answerId=23455729022#23455729022

That problem lasted about a week and then my phone began working again, except I noticed a white line of light running diagonally across my screen. It's fairly light so it doesn't bug me and I just let it go. Then, this morning I noticed a new problem. When I am in an app for more than about 5-10 seconds, thin, gray lines appear in a grid on my screen. When I back out of the app, there are a number of darker, thicker gray lines at the top of my screen, and my touch screen no longer works. I have to lock and reopen my phone to get the touch screen to respond again.

Does anyone know what this is or how to fix it?

Also, my phone is fairly new (few months old). I have never dropped my phone and, as far as I know, it's never gotten wet. I checked the water damage sensor and it is completely white and shows no sign of water damage.