Your .h file declares the variable glActiveTexture. Even with header guards, this means that when this header is included a new definition of the variable is created. To solve this, define the variable as extern and then define it in a single .cpp file of your choice.
I.e.
// .h file
extern PFNGLACTIVETEXTUREPROC glActiveTexture;
// .cpp file of your choice
PFNGLACTIVETEXTUREPROC glActiveTexture;
This tells the compiler to not create a new definition whenever it reads the header code, but to resolve it when linking. One of your .cpp files then provide this definition explicitly and the linker is happy.