Or the fonts might simply be fonts installed at your school, not at home, and not available through Typekit.
I'm sorry that you ran into trouble with this. The Creative Cloud desktop application is the program that you use to install your Creative Cloud programs (such as InDesign) and manage your files and font selections. It looks like this:
If there are problems with font sync, there will be an error listed in the Assets > Fonts tab of the Creative Cloud desktop application.
Please check these troubleshooting steps for desktop sync, which cover most of the common problems:
If those steps don't get font sync working for you, you can email Typekit Support directly at email@example.com for further help. Best,