Here, read this thread on how to change classes and where to find them :
You select online play or solo, select a mission... next screen, the game let's you either play the mission, change character or change class.
Just between the line favourite character and ready to play, there is a line CHANGE CLASS.
Connot be more clear. If you keep saying there is no such thing, then you clearly should desintall the game.
The other screen to upgrade weapon/classes, you need to press R1 to get to it. That's not where you change class, you can only upgrade your weapons and classes.
You have a screen to level up weapons and levels and a screen to select character and class.
The first screen that allows you to change character, allows you to change class.
Just read the line just under "Favourite Character", you will see the "change class" option.