Is "ego sum magistram" also correct?
No, the forms of "to be" - here "am" - requires nominative case for both the subject and the coupled word.
Wouldn't this be teachress?
Can't say I have ever heard that where I am, we just use teacher, regardless of gender.
Based on a quick look on wiktionary it claims it to be 'archaic except in India' however, someone may know more about its usage.