Changed it into drive and then my car started shaking violently?

Hello,

This could be due to a number of reasons.
It could be that the CV axle is damaged or disengaged or broken. Also, it could be due to internal failure of the transmission.

The best course of action would be to do an inspection of those components.
Look for any damage to the CV axle. If the CV is damages, you might get grease leaking out of the boot.
It will also be a good idea to inspect the intermediate shaft.

https://www.2carpros.com/articles/replace-cv-axle
https://www.2carpros.com/articles/clicking-sound

I have attached diagrams for your reference.

Please let me know if you have any questions.
Thank you.