AC needs to find the library parts you are using. So they must be loaded in the library manager.
If you save it as an archive file, all used object are stored in this file (*.pla). When you check your library manager, you will see this archive file is used as library.
You should not continue saving back and forth as pla. Just save it as a solo project (*.pln) and load the AC 13 library at school again, replacing the archive file.