First, some teal deer:
1) You have to know what the rules are before you break them. Art has a ton of fundamental "rules" (or "guidelines") that you as an artist must learn, just as a writer should know spelling, grammar, character archetypes, basic plots, a touch of literary history and so on, before he or she ever writes their first story. Look in the art portfolio of anybody famous, regardless of art style, and you'll find tons of practice art using the rules before they go experimenting.
2) "Distinctive style" implies an internally consistent set of rules, either on top of, or in place of, rules imposed by other styles. Mickey Mouse, for example, looks nothing like an actual mouse, but ol' MM as an iconic character has very VERY strict rules about how he should look. I got to visit an animation studio that did a lot of Disney's gruntwork for "Micky Mouse Clubhouse", one of their 3D cartoons. Pasted all over their walls were tons of reference pictures for how Mickey should look and move. The animators had to redo scenes all the time because somebody somewhere got the tiniest thing wrong. Or, if you think Disney are a bunch of dogmatic evil overlords, take the Looney Tunes for another example. Yes, they break the laws of physics everything all the time, but only as part of a gag does common sense get thrown out the window, and sometimes not even all at once. In the non-comedic scenes, the normal rules of reality are generally implied to have their hold on characters. In fact, what's the biggest joke of "What's Opera, Doc"? That unlike every other Bugs vs. Elmer short, Elmer succeeds in "killing the wabbit", but is stricken with grief as a result. Then Bugs "wakes up" briefly at the end to deliver the punch line: "Well, what did you expect in an Opera? A happy ending?"
3) Think 3D, draw 2D. Things that exist have actual volume. To give verisimilitude to your character, you should think about how they would take up space as a real person. That means, again, learning the fundamentals of perspective, negative space, and composition (for all objects), as well as anatomy for living things.
4) The illusion of life is just as important, if not more so, than the illusion of reality. So you've done your homework, slogged through all of the practice (yes, it's going to be boring and tedious at some point), and decided that you're going for a more cartoony way of drawing. Fine. But your characters still have to feel "Real", not in the sense of "They Actually Exist", but someone looking at your picture can think: "Oh, wow, I could totally see this dude doing this!"

So, now that you know what my "grading" rubric is, let's take a look at how you measure up:

1) Fundamentals - I don't have a body of work to judge you from, but just by this picture, you seemed to have tried learning to draw straight from copying Your Favorite Artist without really understanding why they have done a certain thing in a certain way. Your picture parses into a portrait of a person solely on the merit of the human brain's ability to interpret images, especially that of human faces. Grade: Insufficient.
2) Internal Consistency - This one, I won't grade you on, since you only have this one picture. But I'd like to see more of your work.
3) 3D, not 2D. Let's break this down in sub-sections...
3a) Anatomy. Your character has nothing that approaches human anatomy; rather, he looks more like a puppet. If, however, he's supposed to be a puppet, then he's lacking in actual puppet parts--an opening in his back (or somewhere) for the puppeteer, and something to let said puppeteer (and/or assistants) to manipulate his hands and feet. Grade: D (for human), C- (for puppet).
3b) Volume - Though they lack proper proportion, your character does have some suggestion of volume, though if I were to be super nitpicky I'd dock you points on the wine bottle. There are also pose issues that I will address in more detail on point four. His head, however, confuses me. The entire back of his skull seems to be missing, and yet you imply by the lines of his eyepatch that at least some of said skull should be visible. The mouth should not be a horizontal line but an arc suggesting the curve of his head (yes, even for puppets whose head is literally box shaped--the curve at the edges should, in fact, be even more extreme). Grade: F (human), C- (muppet)
4) Illusion of Life. This is graded by looking at your character independent of all of the above, but I'm afraid he still doesn't cut it. This is an incredibly boring, static pose. If this is supposed to be for his "character design", then he should be standing upright with legs together and one or both arms stretched out, either in a perfect "T" pose or with "airplane arms" (arms stretched out in a 15-degree angle). If, on the other hand, this is supposed to give us some idea of what his personality is like, then his body language should reflect that. A more relaxed or drunk character wouldn't have their limbs in such a straight, symmetrical manner. (Don't believe me? Try this pose yourself. You'll find that it's incredibly uncomfortable to hold it for a long time and would immediately want to shift some body parts around.) Or, back to the "puppet" explanation, he doesn't look like a puppet that someone left somewhere, either. Try throwing some ragdolls around in Garry's Mod if you have it--or, if you don't, try throwing around some actual dolls made of soft material. Even the most perfectly arranged ragdoll is going to flop around because it has no muscles to hold its parts up. Your puppet is magically animated, you say? There should still be some "hint" as to its mundane ragdoll nature, such as button eyes or stitching where the joints should be...etc. Grade: F (human), D- (puppet)

Overall comments: You might have well overcome a lot of obstacles to get to this point. In that case, good for you. But you still have a long way to go.

Final suggestions: Learn, learn, learn those fundamentals and practice, practice, practice them. It'll get tedious as hell, but the payoff is more than worth it. As someone who loves to draw, one of my lingering regrets is that I basically learned everything backwards, and developed some very terrible habits as a result. To use another metaphor, even if you don't plan to be an Olympic level swimmer, you should still learn how not to drown if you ever go into the water, and jumping head-first into the deep end is a pretty inefficient way to avoid a watery grave.