My iPhone keeps tapping other things when I tap something different?

I have an iPhone 5C and every time I tap something it doesn't click what I want. It usually just hits the whole different side I tapped on. It gets really annoying I have to lock my phone and unlock it a couple of times before it goes back to normal and it only lasts for a few minutes. I also have these grey marks on the top and bottom of my screen and I'm not sure what they are and I don't know if that's what's causing this to happen.

Your digitizer sounds like it's broken. This is a pain in the ***, because it means you either have to open the phone up and solder in a new one, (a skill and tool most people don't possess) or get the screen replaced entirely.
Talk to the nearest tech support place, talk to your provider (Verizon, etc.), and talk to the person who'd be replacing the screen if you decided to and see if you can get a consensus.