So if it were me I would take there backpack rule and shove it in their greedy over protective faces.
This is not a loving BACKPACK you dip stuffs.
This teacher obviously has a personal vendetta against you, otherwise she would have let it slide LIKE EVERY OTHER TEACHER YOU HAVE.
I mean it is one teacher that is having this pain in her ass over a small laptop case.
You're a bad teacher if you do this stuff to a single kid. If she is a cunt to all of her students fire her.
But ya if they ask why you have a bag when the rules state no backpacks. Just make it very clear to them that Backpacks is a single item to carry things, it never stated you couldn't bring book bags, or laptop cases, or large binder cases.
Honestly you just need to approach it all in a non offensive-calm way. If you get severely emotional like your butt hurt suck up of a teacher than they might not take you seriously.