How do I get my iPad's touch screen to work after updating 16.1.1?

After ANY iOS/iPadOS upgrade/update, you should ALWAYS perform a simple hard reset/forced restart of your Apple mobile device.

For iPad models with a Home button, do a simple hard reset/forced restart of your iPad by holding down both the Home and sleep/wake/power button simultaneously until your iPad goes to black and restarts with Apple logo, then release the buttons.

OR

For much newer design iPad models, without a Home button, try the new simple hard reset/forced restart procedure for the new 2018-2022 iPad Pros, 2020/21 iPad Air 4 and 5 and 2021 iPad Mini 6 models.

1. Press and release the volume button closest to the top Power button

2. Then immediately press and release the volume button farthest from the top Power button.

3. Then, press and hold the top single sleep/wake/power button You will see the Slide to Power off button, but keep on holding down the power button until you see the Apple logo, then let it go.

Once you have performed all the steps, wait for a few seconds and your 2018-2022 iPad will boot up completely to the iPad’s Lock screen.

Best of Luck to You!