Math is not necessary for many kinds of programming. Yeah, some algorithms make occasional use of graph theory, and there certainly are areas of programming that are math-heavy (3d graphics, perhaps? Also, stuff like Google's PageRank algorithm uses linear algebra), but there are huge swaths of software development for which no (or little) math is needed. In fact, just to hammer on this point, I distinctly remember sitting in a senior-level math course and overhearing some math majors discuss how they once took an introductory programming course and found the experience confusing and unenjoyable. So yes, math and programming are quite distinct.

The probability I would place on you being able to make a living doing programming is dependent on only one factor: your willingness to spend your free time writing code. There's plenty of people with CS degrees who don't know how to program (and, amazingly, don't even know how to FizzBuzz), and it's almost certainly because they've never spent significant amounts of time actually building software. Programming is "how-to" knowledge, so if you can find a project that motivates you enough to gain significant experience, you should be set.

I'd guess most people fitting that description won't make a living as programmers, but the good news is, you don't have to guess in advance. Just try it and see if you get in to it. You're very unlikely to regret it whether it turns into a living or not.