Am I eligible to work as a teacher in a government school?

Yes, your qualification is sufficient to be employed as teacher in government schools provided that you have cleared any entrance or eligibility test (if organised by that state or central government). I would suggest for further promotions or for high salaried teacher job pursue any master degree.

Yes, all your qualifications are enough to apply for a post of teacher in government schools. Look out for the position in the newspaper or online and apply.