Does a certification in ESL (in the state of TX) cover any requirements regarding TEFL

I will be graduating in May with my Masters and certifications in EC-6, ESL, and PPR (passed all 3 state tests). I was wondering if this covers any requirements regarding TEFL? I have not been given my certifications so I am unable to post them (I will get them in May, once I graduate). Also, does student teaching and subbing fall under "teaching experience" for TeachAway?