In high school, you may get syllabi; short summaries of the course you are going to take. Having a binder and a handful of pencils and pens is usually good. You may also be assigned a textbook. If you would rather balance all these things on your head, then go right ahead and do so (no pun intended. But if you end up not using your backpack, then it probably has almost nothing in it, which shouldn't be that much of an inconvenience. And in high school, you are rarely ever going to be the only one who does something.
Also, school isn't a fashion runway. What you wear isn't the important thing. Being prepared for class is. If you have your outfit picked out, but are still wondering whether to take a notebook and a backpack, then you need to get your priorities straight.
