Do you want to spend your time making games, or making tools and libraries?

The existing libraries are already built and debugged. Some represent years of work, some represent work-decades or even work-centuries from large teams of experts and specialists.

There's nothing wrong with doing it all yourself, but don't expect to be making great games when you go that route.

C-Research said:
Tomorrow I begin downloading everything, building, and installing, I am on Linux, so some of it must be built from source, which is easy for me most of the time.

I'd start by just using the package manager for getting libraries, dev-tools, build-tools etc etc. In my experience you have to go into a very niche area before a package manager of the major distributions doesn't have a pre-built and maintained answer for your question.

For 2D sprites, I'd say libpng will work, although you may not even need to handle that yourself, as pretty much anything that produces or needs 2D sprites understands PNG files.

Why does it have to be C? I see from time to time people are interested in developing bigger applications and games in it, but why? I had my first job in C and tried to build software in my spare time using it as well. When I left for other jobs with other languages I realized how tedious it was to code in C and how futile it was to try to build something that runs on a desktop computer in it. If you want to see what you are in for you should look up Randy on Youtube. He had a prototype in Unreal Engine 5 years ago but decided to start over with C. I think he uses the engine made by the creator of Handmade Hero. From the looks of it he is just now starting to get to the same point as he was 5 years ago with the project on this engine. A more experienced developer would of course have gotten to that point a lot faster, but developing games in C coupled wtith not knowing much programming beforehand seems like a long road to travel.

C is of course still running strong in bare metal embedded and operating systems but it's pretty niche these days. I am more in favor of structural programming than OOP and I like the simplicity of C so I'm not saying this as someone who dislikes the language. It's just a bit dated at this point and has very limited tooling.

C is a downright bad language for reusable high-performance algorithms. The main problem with C in this area is that it has no good way to express algorithms generically, without tying them to concrete data structures. Compare C's qsort with C++'s std::sort. Both express the same basic idea, but the latter is both much faster and much easier to use.

There are areas where C shines, and I use C libraries all the time, but reusable high-performance algorithms really isn't one of them.

C-Research said:
I am strong in math. It is much more efficient for me to depend on my math skills, rather than learning another coding language such as C++.

My bet: You totally overestimate the burden of learning some basic C++. I would try it, along any need for it where it comes up.
Basically that's what i'm doing for decades. After using Basic and Assembler on home computers as a kid i had learned C, which felt like the perfect language to me and i was happy with that.
I learned about C++ soon after that too, but initially used only a few of the new features. Sticking at a C with classes style for many years, it did not really change much for me, nor did i adopt a general OOP paradigm shift.
Only in recent years i started to understand modern C++ better, making my life a lot easier actually. It really helps with producibility and maintenance once the projects become larger.

My point is: You can approach this slowly, pick up only what feels useful right now. Nothing forces you to use or know all features. No big deal, not hard, not much effort.
But - by actually using the language, there is no more barrier to use libraries written in it, or to learn from C++ code of others. APIs are usually in C anyway, or require only a very basic amount of C++.
So you can be still a C programmer at heart, and you can keep your effort on programming languages as low as you want. Imo, it's not the most important thing anyway, just C alone is indeed quite old school, you know ; )