"I'm right, aren't I?"

Yes, it is common. The little-seen "amn't" does occur in Irish and Scottish English.

There is a good article on this at Wikipedia:

Amn't as a contraction of am not is known from 1618. As the "mn" combination of two nasal consonants is disfavored by many English speakers, the "m" of amn't began to be elided, reflected in writing with the new form an't. Aren't as a contraction for are not first appeared in 1675. In non-rhotic dialects, aren't also began to be represented by an't.

Lower down the page, there are the following sentences:

Aren't as a contraction for am not developed from one pronunciation of an't (which itself developed in part from amn't - see etymology of ain't for further discussion). In non-rhotic dialects, aren't and this pronunciation of an't are homonyms. For reasons that are unclear, the spelling aren't I began to replace an't I in the early part of the twentieth century […].