Is it possible to use OpenGL purely with C instead of C++? I am wanting to make sure there won't be any problems with my using C and not C++. OpenGL does not depend on any C++ libraries right?
Yes, in fact OpenGL is a C library. You can perfectly use it with C.
OpenGL can be used in C. Some libraries can't, though. For example if you want to use GLM you will have to use C++ instead of C.
OpenGL is a C library, which means that it's made with and for C, so of course it works with C. The reason why it also works with C++ is because C++ is actually nothing else than C with some things added so any C code is also valid in C++. So OpenGL uses C code which is also valid in C++, and it doesn't use anything that is specific for C++.