As others mentioned you need to replace the LCD Screen and Digitizer which come as an assembly. I would not recommend trying to replace one without the other.
TIP: If you just need to access the phone. You can connect a regular USB mouse with an OTG cable.
Also if you have the opposite problem (where the touchscreen works, but you can see it), you can use a SlimPort to HDMI adapter to see the screen on a monitor. I don't think you can use both an OTG and SlimPort at the same time.