You don't have privellages in phpMyAdmin to create databases this has to be done through the cPanel.
The error that you are describing is from an invalid mysql username and password. Be sure that you have the database name, username and password correct and note that the username and dbname require your 8 letter bluehost username before it.
Also be sure that you have added the user to the database you are trying to connect to in the MySQL section of cPanel.
I may not be smart enough to do everything, but I'm dumb enough to try anything.
PS I no longer work for Bluehost, any posts from me may not be official company policies or views and should not be associated with Bluehost.