Where can I get a cute bag to use as a school bag.( I don't want an actual backpack)?

You could use a cute messenger bag like the Harajuku Lovers Fan Cross-Body Bag.  This is very colorful and cute.  It is made from synthetic fabric with canvas trim.  It can hold lots of stuff so it would be perfect for school.  There is front exterior pockets and rear exterior zip pocket.  The top has a hook and loop closure.

You could get a cute tote bag like the Miquelrius Jodi Labanda Butterflies Large Tote with Leather Handles.  This bag has got a great design.  It is made of polyester fabric and has leather handles.  This does have a pocket inside to hold more stuff. 

Or you can get a duffle bag like the Wildkin Girl Rodeo Duffel Bag.  This is made of polyester.  It has an external zippered compartment with detachable padded shoulder strap.  It has plenty of room for all you need to take to school with you. 

These are just some recommendations of which you could use instead of a backpack.  There are lots of great designs for the totes, messenger bags and the duffel bags.  I hope this helps you with your search.  Thank you for your question.