>>8>>17>Use C because X uses CPlease. You wont impress ladies with you C knowledge, even less your employers. Know which language to use when.
C is mainly used for libraries who need to work on a wide range of devices. If a piece of hardware does not have a C compiler then it is irrelevant to what you are trying to do. And it is also used if you want the ability of having bindings to a wide range of different programming languages for your library. That is why SDL, GLFW, ect... are programmed in C. But you should not C on top of it
If you can, prefer C++ over C, (unless you want to achieve the above). Because:
1. If you have a decent C++ compiler it's almost as fast as C to the point where it is negligible.
2. As your project becomes larger it will become harder to manage and debug. Especially for inexperienced programmers.
3. It's much faster in development speed.
In the end you write code for humans to understand, not for your PC(it's your compilers job to translate). You just have to find to right balance between layers of abstraction(speed of development) and speed at which it runs. For games who need high performance C++ is the best choice.
Now here is where OP is confused.
If you want to _MAKE_ games you should learn Unity or UDK. Making engines is just for collage students and million dollar companies. It's cheaper, faster and a whole lot better in every way to just buy a license for 3rd party engine. You can make games with little to no programming knowledge needed.
If you want to _LEARN_ how games work then you should indeed learn C++. Since you say you already know C# the switch wont be that hard. Learn the language and then i suggest you read these books:
The c++ standard library, a tutorial and reference (978-0201379266)
C++ Coding Standards: 101 Rules, Guidelines, and Best Practices (978-0321113580)
Start with this, if you're still interested come back and start learning OpenGL and Direct3D.
Also, yes you are going to need math. Especially when you're going to get into writing Shaders. Vector math should become as easy as 1+1=2 to you. If it is not, visit KhanAcademy.