I definitely agree with @ScribbleJay on everything, don't cut out the backgrounds.
Do you have any comics you like, that you feel like have that polished look you are looking for?
I would say to look at them more closely.
Do experiment with styles more! It may not help in the beginning, but try doing more different style: use another types of body, another faces, another eyes. Maybe the problem is that your characters have these cute round tubbies and their hands and legs are oversimplified and look like mittens and kid's sliders? The characters just look very childish, they have toddlers anatomy, and they look like they are wearing not usual clothes, but slide-in alternatives.
I'm not saying here that it's bad, but if you feel like your art is looking like it's made by child: it's that, when children draw, they don't know better and don't know how to draw proper hands or clothes, that's why they oversimplify everything. So maybe all this that is what's giving you that thought too.
I would say try to go for a more complicated body, clothes and limbs (maybe look at Pigeon Gazette or Sarah scribbles for more inspiration, or every other comics you like), look on chibis by famous artists, like chibis from Hetalia. Compare your every new sketch with all the different styles you tried until you have a result you like.