I hit the brake my steering wheel starts shaking violently

Yes. You have a brake pulsation and the rotors need to be replaced.

Here is a guide that will help with this:

https://www.2carpros.com/articles/how-to-replace-front-brake-pads-and-rotors-fwd

Below you will find the process from the manual that will help with replacing the rotors and pads as I would replace them both at the same time.

Please run through this and let us know what other questions you have.

Thanks