The GPL doesn't "infect" things. It merely requires software that uses it to be free software. For instance, you can extend GPL software, and dual-license your extension under MIT and GPL, though the GPL applies as long as your software is using the GPL component.

In this case, the software you've written to extend the GPL, is not "infected" by it.

It does not REQUIRE you to use only GPL, it requires you to make it AVAILABLE under GPL.