Welcome Katie Jane Németh,
Thank you for providing the detailed troubleshooting history. From your description, I can see you have already tried the common icon-cache repairs, so repeating those steps would likely not help.
Before we go further, I need to clarify one point:
Is this laptop signed in with a school account and managed by your school's IT department, or is it your personal Windows device using only a personal Microsoft account?
I ask because you mentioned that you do not have administrator access and the device is school-managed, which may place the device under organizational management rather than a personal Windows setup.
Looking forward to your reply.