I am trying to include a library for an Arduino project that includes a .h and .c file.
Rename your .c file to .cpp and see if it gets any better.
Because unless your .h files includes "extern "C"", the .ino file (compiled with C++) will assume that the functions in it are C++ functions, and apply "name mangling" depending on the function signatures.
Ie: a pure C library needs some additional work before it can be used in C++ code.