Coming from a "No Name" University outside the US, what are my chances for admission
At least in my department/school in the U.S., we have several individuals from African countries studying for doctoral degrees. I'm a little concerned that there seems to be a disconnect between what you say about your performance (above average) and what your professors are saying (no one would want someone like you, possibly because of where you studied). 

As far as I can tell, most schools in the U.S. encourage individuals from diverse backgrounds to apply for their programs, including graduate school. So, I would not make a blanket statement that your country of origin and/or background is an immediate disqualification. 

Regarding your academic background, even U.S. colleges differ in terms of academic programs and rigor. That is why the graduate school admissions process involves many different parts, including standardized test scores, interviews, and/or letters of recommendation, that help the admissions committee get a more complete picture of you and how you may fit within the program.