I want to point out that there are, topicwise, different paths from the most suggested standard one:
As noted by "jmoy", time is limited - the comments telling you to learn some physics or programming first or on the way seem to ignore this somewhat. Sure it is good and will pay off to have these things as background, but it is not indispensable. Apparently you already have discovered your fascination for mathematics, so you don't have to back it up with these things that surround mathematics. Physics and programming can give you good intuition, but so can doing mathematics itself.
Also, going through the whole standard curriculum with lots of calculus and coordinate geometry is by no means the only way to come into mathematics!! Certainly a basic knowledge of these things will be indispensable at some point. If you actually enjoy studying calculus, then do it, it's an excellent start! But don't just do it because it is the standard curriculum in US colleges. Often people who went through this can't imagine having learned things in a different way, but that is perfectly possible, and normal in many countries (I went through a German school and university and learned much less calculus on the way than an average US student - it didn't do me any harm).
After all you are wanting to study mathematics for having a rewarding experience, and while there will be some frustration on the way, it should feel somewhat rewarding right from the beginning.
So here are three alternative routes - in case they pique your curiosity more:
Number Theory is a field which seems perfect for self study: It is concerned with objects that you know very well already - the natural numbers - yet it is a deep and difficult field and connects to virtually every other part of mathematics. This is mathematics of an entirely different flavour than you would see following the calculus path, and it can bring you just as far. In particular it will bring you to a point where you want to study calculus because it tells you things about number theory.
For this road, pick up a book on Elementary Number Theory (e.g. (1), free for download - but if it's too hard going, there are more basic ones also) and work your way through that. Accompany it with the book "Fearless Symmetry" (2) an excellent popular math book, and not a waste of time! It leads you very far into things which connect to current research (the so-called "Langlands program") but is very friendly written. It gives you a path to follow; you get intuitive ideas for example about "group theory", and whenever you get to such a point where a new concept (like "group") is introduced, you should accompany it with a more formal treatment, where you can see the basic theorems about that structure and get some exercises to solve. I suggest Michael Artin's "Algebra" (3) which contains all you will need to know for a long time on this way. It starts at a low level, which either is already ok for you, or will take only little intermediate reading to bridge the gap.
(If you start wondering when the calculus comes in, pick up Serre's "Course in Arithmetic" (4) and jump to part II, but only after you got some feeling for what's in the first half of Artin's "Algebra")
Combinatorics (e.g. with the book "Proofs that really count" (5)) - this is also a topic which needs no motivation from physics or any other area about which you would have to learn things first. As in number theory you can see how one develops mathematical reasoning to answer questions that make sense immediately. And again it can lead you the point where you want to study other mathematics, e.g. calculus, because it makes sense to pursue those questions in the context of what you already know...
Logic, e.g. starting with Carnielli, Epstein: "Computability" (6) - this is a basic introduction into logic and computabiliy theory, written for philosophers, and therefore starting very gently. It also paves a way into mathematics via a motivating question - When should we call something "computable"? - and leads you all the way to a proof of Gödel's famous undecidability theorems. Again this is connected to a lot of mathematics. Maybe you would after that like to go on studying non-classical logics, which will lead you to algebra, lattice theory and topology...
Whatever route you choose (and I have to emphasize again that the calculus route is very good as well, if you feel like it), talk to people about the things you study, ask and answer questions, e.g. work as a tutor, or spend time here in the forum!
Enjoy your journey to mathematics!