Car won't move after shifting to reverse or drive. Was working fine yesterday!

Hello! I have 2021 Chevrolet Malibu at 80k miles, automatic transmission, 4 cyl. Was just purchased last year, and till around an hour ago, not a single mechanical issue.

When I started the car, I noticed the check engine light was on after never being on. Then after shifting in reverse to move out of our drive way, it wouldn't move. Pressed the accelerator, also wouldn't move (and yes checked the parking brake). After this, tried shifting to drive, and noticed the whole car violently shook (like hitting a pothole) and made a jarring sound as well. And again the car wouldn't move on its own, and after pressing the accelerator.

Final thing to note, after turning the car off, we popped open the hood and heard the motor continue to run. This occurred for around 10 minutes before it turned itself off. We have been routinely (around 3-4k miles) taken the car for oil changes and just did an air filter replacement about a couple months ago.

Any advice would be greatly appreciated, already fearing the worst that its probably a transmission failure, looking to see if we can do something about it before the repair shops around us open on Monday. Thanks!