There's a lot of things that could be happening in this kind of situation. Here's a trick if it's a software issue. If it's a hardware, then you're gonna have to get that screen replaced.
Firstoff, power off your phone. Then hold down your power and volume down key.
In a moment, you will see a dead android on his back, accompanied with some menu options. Use the volume keys to navigate, and the power key to select. Select Recovery Mode.
From there, select Wipe Cache.
After that, select reboot/restart, and your device will restart normally. Hopefully, it'll work.