First guess here is you likely need a new screen. Although the digitizer (touch screen) and the OLED display are electrically separate circuits, they come bonded together as a single assembly. As such, it's entirely possible for one of them to fail yet leave the other one fully functional. Both components have delicate connections between the flex cable connecting them to the motherboard and the glass the circuitry is printed on, and unfortunately it's all too easy to damage those connections, especially as a result of a drop.
In your case, it sounds like the particular touch screen you use to open the phone has failed. Although you might think it's possible the fall dislodged the digitizer's connection to the motherboard, in practice all of those connectors are locked down with screws and we virtually never see them work their way loose, so as I mentioned the fix for your phone is almost certainly to replace the screen.