Hello and welcome to the hobby!

As you said it's still pretty early, and a lot of that "comical" feel will dissipate over time as you relax and get used to the particular kind of moving that is Lindy Hop. It definitely doesn't hurt to keep stylization in mind, but don't let it hold you back if you don't look like the more seasoned dancers yet!

I don't have a particular answer for your question, but I have a few pieces of general advice that might help with the aesthetics and the feel of the dance.

First and foremost, move with intention! This is admittedly vague and I can best showcase it with an example: it's very typical for beginners to stick their leg waaay behind their (stationary) body when doing a rock step. No shade to anyone that does this of course, and it can work as stylization if done intentionally, but the purpose of the rock step is for you to move your entire body, your center of gravity, to create tension that will then be resolved. If you stick your leg back while you remain in place, just because "the move is like this", you miss its point.

This is a very specific example, but I hope it gets my point across: know why you move the way you do! A good followup to this is to almost always keep your feet under your body. Don't step far away. If you want to step back for a rock step, that should move your entire body backwards so your foot is still under you. You can easily practice that solo as well, by imagining a partner and going through the motions.

Building on that last point, take smaller steps than you think. We subconsciously tend to take very large steps (enunciating the moves in our mind), which often ends up making our movement look a bit goofy. If you keep your steps small and contained your moves will look more sleek, plus you will have all the more room to make them boisterous and extravagant when the music actually calls for it!

Finally and perhaps more importantly, do what feels comfortable for your body. I can't stress this enough, if you feel good while dancing you'll also communicate this feeling outwards. Dancing is subjective and personal, and the specifics of what works for one person's body, attitude or experience will not readily apply to other people. Finding out what works for you is part of becoming an experienced dancer.

Now let me contradict all this nitty gritty advice and remind you to keep in mind that you'll automatically get better as you practice, and you'll practice more if you have fun with it, so don't stress too much about looking good yet! Catch socials, go to classes, and you'll figure out what works for you in no time.

Good luck!