Hello liz!
Welcome to EF!
I read your post. I am a non-native speaker of English, working in Japan as an English teacher. I have only 3 years of experience in teaching English and Science. I did my degree (BSc) in Medical Science. Later I studied B.Ed and M.Ed. to become a teacher. In my country our education is in English medium and English is very common in use.
I came to Japan about 2 years ago. My first year of job search was very much frustrating here as I always got a negative answer for not being a native speaker. Anyway, now I am working at a school. After reading your post I was lost in my past days. I don't know if your degree is valid as a degree for your working visa in Japan or not, but if you try your luck here perhaps you can get good chance to teach English here (perhaps medical English too).
Thanks for reading my post
Regards,
Meg