Teaching English in asia?

I am currently a university student. I was wondering if i could go oversees and teach english in another country after I graduate. i have been looking at the requirements, some programs want TEFL certificates, which im sure I can get. My question is would i be able/allowed to. English is not my first language, I did't learn English till about the first grade. I do have a slight accent/lisp, but english is my primary language. The programs I see only want native English speakers, and im not sure if that includes or excludes me.