Getting your skills to a professional level in ANY field of work takes years of practice...
And with field of work, I mean being an animator... OR a character designer.... OR a 3D modeller... OR a 3D animator.... and so on. You get the gist of it.
There are some very talented, very hard working people that are able to become competent in many fields of art creation at once. Not every Indie Studio seems to have their own animators, or concept artists AND artists working on the actual game art. Especially in 2D, things are not THAT much different technically, and even a lot of 3D artists seem to try to master multiple stages of the pipeline.
Now, 2 things:
1) What you show here is pretty much HIGH-END 2D Art... I really appreciate people setting themselves high goals (guilty of this myself), but be prepared to face the fact that YOUR animated characters will NOT look like that for many years. It is a good end goal, but DON'T SCRAP whatever you produce with your current skill just because it doesn't match your end goal. This will not only crush your motivation because basically you scrap everything until you loose all motivation, but it will also slow down your growth.
Instead, experiment, see what you can do with your current skills, stay open to what other people do to become both more skilled, and more efficient. Work with simpler styles, learn to live with the errors you currently produce in your art.
Finish something, and be proud of what you are capable to produce. This will give you the motivation boost to keep going, and teach you way more than scrapping your stuff halfway through.
2) No school alone will teach you art. Yes, school is always good for learning some basics... more than that, school is an ideal place to meet likeminded people, exchange ideas and skills, and maybe find friends and teammembers to work and learn with beyond school.
The important part is what you do above and beyond just attending school. Real work projects in any school and subject are rare. And any skill, especially art, is not learned from theory.
Instead, you need to spend 1000s of hours drawing, painting, animating things. Produce something, make mistakes, learn from it, get better. This is where you will turn from Noob to Pro, not when listening to some color theory in school.
That doesn't mean that school has no value... quite the opposite. Apart from some basics (which you COULD learn on your own if you have the selfdiscipline, basics are seldom the most sexy subjects to grind through) you will earn a degree, that might open up a lot of job opportunities you wouldn't get without it. So if you want to work as an artist, an art degree will be highly benefical.
Just be aware that in art, more than in any other subject, without a good portfolio of your own work (for which just school work will most probably not suffice), the degree is not worth that much.
So, long story short.
You are already knowledgeable in programming. Good. That means you would start farther ahead than when going the art route. Now, the 1000$ question: do you enjoy programming? Or do you enjoy doing art more?
Because with 90% certainity, if you aim doing high-end games, and might they only be Indie games, you will need a team of DEDICATED professionals to produce the needed quality and quantity of code and art. Lone Wolf devs do produce some amazing things, but most of the time they will have to cut corners... or they just outsource what they cannot cover themselves (in your case, doing the art).
So rather than trying to improve where you are weak (art), you could also try to concentrate on becoming as competent as possible where you are strong (programming), get a CS degree and spend some free time on making your coding skills shine and start working on some of your own projects again. If you are good, and network well with artists online or in local art schools, you might even find someone to team up with.
You will most probably reach your end goal of making a high-end 2D Indie game with amazing animations quicker than if you try to cover all bases alone.