The short answer - lots of practice. When I try to do extreme exaggerations, I try to make sure that no matter how large, small, stretched or compressed I make the various features, I still try to draw that person's features accurately. So, it's okay to make the eyes or nose massive. Just make sure that you are drawing their specific eyes or nose and not just general shapes or symbols representing the concept of an eye or a nose.

I love Rick and Morty! I have actually done a couple of realistic cartoon character interpretations in the past. I did a live stream about it last year. https://youtu.be/7jTUngpWIi8

I also don't know what GDRP is and why it would prevent you from uploading a photo of the person. Let us know. The main problem with the rough sketch is there is a consistent skew to its structure. The shapes are "leaning" up and to the right. Especially the jaw, ears and glasses. My guess is you drew this on a flat table (or at least a low angle) and are right-handed. When you create a drawing looking at your paper surface from a low angle the shapes will look fine from that perspective. But when you look at them straight on, the skewed perspective becomes more obvious. If that is not the case and your paper surface was propped upright in front of you, then you need to focus on why you are doing that. Be sure to use parallel and perpendicular guidelines to map out where the features of the face will go.

I brought your abstraction drawing into Photoshop and flipped it to get a better look. You seem to be drawing the rhythm lines with an unsteady and uncertain hand. Remember to draw in long, steady, continuous arcing lines from one side of the face to the other, so that features align with each other. The jawline especially feels uneven. Also, the nose abstraction doesn't seem correct. You need to move it further to the right, relative to the centerline so that the nose looks like it projects out in front of the centerline when the face is turned away like that.

Good use of the Reilly rhythms. They're very well-structured. And it's a solid exaggeration. I'd like to see you take this to the next step with a more finished drawing/rendering.

Taking into account the overall shape and mass of the head, the centerline on the right feels like it's in the best position for the caricature. I would go with that one. But then the nose AND eyes feel incorrect - like they both need to shift to the right as well.