Why does it hurt in the mouth when drinking carbonated beverages?

The typical explanation for the origin of the "sting" is that $\ce{CO2}$ turns into carbonic acid ([reddit](https://www.reddit.com/r/NoStupidQuestions/comments/3mx5jk/why_does_the_fizz_in_carbonated_drinks_hurt_my/), [yahoo](https://answers.yahoo.com/question/index?qid=1006050228925)), however the "explanations" there are incomplete.


The answer I'm looking for would cover:


1. Is conversion to carbonic acid is really the case here? And what are the original compounds the same enzyme(s) is used for?
2. Why is there no "sting" from $\ce{CO2}$ found in air?


