To be able to teach English in Mexico, you should obtain a TEFL certificate first. Teachers of English are allowed to teach legally only with such a certificate. It is not very difficult to get the certificate - most colleges and learning centers offer short-term programs that can earn you your certificate in a matter of months. So you should better get the certificates.
You need a work permit to be able to work as a teacher of foreign language in Mexico. Your immigration papers need to be in order, because working illegally in Mexico can be dangerous as you can send out of the country. Keep in mind that most Mexican work passes are good for only up to six months; but everything is possible. Even entering the US for a matter of hours will reset your pass, and you'll be able to re-enter for another six months.
Requirements for the applications to the newcomers in Mexico English language teachers are sometimes inconsistent, so it is advisable to be prepared beforehand. You need to gather all possible documentation, including birth certificate, college transcripts, reference letters, and other paper confirmation of your possible achievements. It's difficult to predict what you'll be asked for, and you'll want to spare yourself the expense and trouble of having to return home for something you didn't bring.