I am not sure that your journey is all that unconventional. It is entirely normal that we try a bit of this and a bit of that before we figure out what we want to do with our lives. Your journey may be a bit unusual, but so was mine, and so was the journey for the next person that you happen to meet. Your journey, and how you think about it, does make sense.
Also, one thing to keep in mind about software engineering: Writing software is largely about showing computers how to do things that people used to do, or that people used to wish that we could do but we couldn’t because we didn’t have the computational power or memory. In showing computers how to do things, a bit of this involves a computer language, a lot more involves knowing how to structure software and problem solving, but a huge part of this is understanding how to do something that humans typically do. Thus this might involve art, or physics, or math, or finance, or just about anything else. Since there are so many things that we are teaching computers to do, there are that many things that someone somewhere needs to understand very solidly before we can show the computers how to do it.
And “making technology personable” is huge. No one wants to use a computer system that is tortuous to use. Computer systems need to be tailored to the user.
To me your description of your path makes a lot of sense, and serves as a strong motivation for what you want to do next. This motivation can help a student do well in university. When a university is a lot of work, it can be very helpful for a student to understand why they want to put in that effort consistently over several years.
Depending upon how much math you do have, this could be an issue. You might need to take some relevant math courses, for example at a community college, before starting university and quite likely before applying. How much you need might depend upon what level of university you want to be starting at.
Edit: One thing that is worth adding. Math is a subject where what you are learning now often depends upon what you learned last year and the year before, and what you will be learning next year is likely to depend upon what you are learning now. This is an area where understanding the prerequisites is important. You will probably want to carefully evaluate what it is that you know and what it is that you don’t know in order to fill in the blanks properly. This might take a bit of effort to figure out but is likely to be worth the effort.
If you are intending to be a regular undergraduate student for four years at a top high-tech-oriented university, then you might for example want to at least be ready to start taking calculus when you show up at university. This would suggest the need to fully and solidly understand the prerequisites for calculus, including high school algebra, trigonometry, and pre-calculus. If you are going to be coming in with one or two years of credits, and hope to get a bachelor’s degree in two or three years, then you might want to have first completed calculus and differential equations. Linear algebra is also something that sounds likely to be useful in your case, but is something that a university can teach you if you are going to spend four years there (I think that I took this at the beginning of my sophomore year of university, and I was a math major – a major that can also lead to any one of a large number of possible career paths).
Georgia Tech is a very high end, very stressful high-tech-oriented university that is full of very strong students. However, there are lots and lots of other universities that are also very good. The large majority of these other universities are not quite as stressful as GT, and not quite as hard to get admitted to. You might want to be thinking about which universities are the best fit for you. There are lots to choose from.