If only I taught a subject that they teach at international schools!
If you do your CELTA then that should suffice. Not every language school will necessarily want someone who has a degree in English language too, though that would help. You have experience of teaching which combined with a CELTA should mean that you stand a good chance of employment. From reading through the threads on here though, you need to be careful of some language schools, and you aren't likely to be earning that much money either.
Good luck!