create new MySQL database and user using OS root credentials
I believe you will need to install another, separate instance of MySQL, configure it to run on a different port, specify that port in your login screen, and then do as you like.

You can do this by simply installing MySQL to another disk location, and then editing the ini file.  On Windows and Mac installations, this is called my.ini

Alternatively, I think your only choice is to get permissions granted to you on the currently installed MySQL instance.  The root password to the OS and the root password to the MySQL server instance are entirely distinct (as I'm sure you know).