hi this is ahmad . I just found that the question tag of I am is arent I . I answered just like you Am I not . but still not satisfied why teachers like michael swan chose to write Arent I . only .
Maybe people enjoy to see themselves as “We” so they say “Aren’t I?”
In my, a learner, opinion, the only correct way for this tag is “Am I not?”.
“Aren’t I, Amn’t I, Ain’t I, An’t I” are all equally good enough or not good enough informal ways to say “Am I not” in a short and fast way.
There is an interesting article at worldwidewords.org/qa/qa-amn1.htm which explains how “amn’t” (the logical contraction) became “an’t” and finally “aren’t”.