Recommended way to fork a library
Almost.


Fork the library to your account
Check out your fork
Edit as needed
Commit locally
Push back to your fork


Your fork is yours to do with as you wish. Github makes it easy, should you wish, to then pass those changes back up to the original repository (make a "pull request"). But you don't have to do that (and probably don't want to).

You can make a new branch if you like, but that's pointless - your fork is, in effect, a branch itself (well, it's an entire new tree really).