It sounds quite likely that you've damaged some of the circuitry that controls the touch screen function, i.e., the digitizer.
Unfortunately, on your model of iPad it's not possible for the average person to replace just the digitizer glass, as it is fused to the LCD display, so the only option is to replace the entire LCD / digitizer assembly.
There are several sources you can buy a replacement screen from, including right here on iFixit.
iPad Air 3 Screen - iFixit Store
If you're feeling adventurous, there's a DIY guide that will step you through the entire process of replacing the screen yourself.
iPad Air 3 Screen Replacement - iFixit Repair Guide
Good luck, and let us know how it goes!
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