Frankly speaking - I've never heard about "amn't" before. Did you think it up?
Aren't is the standard version, but amn't I is very common in Irish English and can therefore be said to be correct in spoken language atleast regionally. So no, amn't I isn't made up, it is just very uncommon outside of Ireland.
Hope it helps.
Yana
I think both are possible depending on the region. But the latter is more common.
My tongue gets tangled when I try to pronounce "amn't".
Not uncommon in my house!
Clive