Whenever your Project is loaded in the Unreal Engine or the Unreal Editor, it can have only one Media Profile active (or none at all).
When you have your Project open in the Unreal Editor, you choose which Media Profile you want to be active using the Media Profile menu in the Toolbar of the main Level Editor:
Media Profiles are Assets that are always saved in the Unreal Engine Project. However, the choice of which Media Profile is active is saved on each computer, not within the Project. That means that once you've set a Media Profile for a given Project on a given computer, you never have to change it again (unless your media hardware or configuration changes).
On the other hand, when you run a packaged version of your Project, the choice of which Media Profile is active is always determined by the Startup Media Profile setting, which you'll find in the Project Settings window under Plugins > Media Profile.