I don't know the reason that I am not" is contracted as "I'm not" but not "I amn't" -- but for whatever the reason, there is no "I amn't" in most dialects of English.
Therefore, you can't do the inverse and say "Amn't I" for questions.
Aren't I good enough for you?
Aren't I the the best person for the job?
I'm going, aren't I?
If they think this is just too weird, they can say "am I not?" instead.