The brown paper bag [1] was not connected to the peanut allergy, it was mentioned as an example of another thing that only (to OP) seems to happen/be a thing in the US.
[1]: https://www.uclahealth.org/news/article/breathing-into-a-pap...
[1]: https://www.uclahealth.org/news/article/breathing-into-a-pap...
It's just a TV/movie prop to show someone having a panic attack, for the most part.