Hi Andrea!
Yep, all of our schools exist in the same world and at the same time, so you would need to make a separate character to play at the other schools (unless you were thinking of transferring your current character away from Beauxbatons and to another school).
And yes, each character needs their own account with their character name as the username.
Each basic (free) site account comes with the ability to link up to three accounts together, so you would be able to work with both characters from one log in. You can get to this by going to your profile summary page. From there go to modify profile -> manage subaccounts -> create/link (button at the bottom).
If you have any other questions or need help with anything, please let us know!
-- Alastair Grimm
