Strictly speaking, "aren't I?" and "It's me" now are correct, and occur more frequently in "standard", even formal, usage than the supposedly "grammatically correct" alternatives, which are consequently less so. They have become fixed idioms, and do not follow the rules applied to other contexts.

This points out that grammar rules are not entirely consistent across the board; "correct" usage depends on grammatical context. We say "You went" but "Did you go?" We say "Did you go?" but not "Did you be?" "Aren't I?" as the negative form of "Am I?" is just one of those things. If you claim it's not "grammatically correct", you don't know what correct grammar is.