Moving photos to a new account

If you already have your new Lightroom account setup and subscribed, you could create a shared album and invite your school account to join that shared album (with Can Contribute or Can Edit rights).  And then from the school account, you could add all your images to that shared album.  The benefit of this is that your edits will be preserved, though of course you can always opt to return to the original unedited state.

Another option: you might want to try the Lightroom Downloader app for Mac or Windows as a quick way to fetch your files and edits: https://helpx.adobe.com/lightroom-cc/kb/download-lightroom-photos.html 

This will copy your files to your computer, and later you can reimport them into Lightroom manually.  However, since the Downloader saved both your original and also your edited work as separate images, importing everything back into Lightroom will appear to have duplicate files (original images + edited copies).  To me, this is less elegant than using the Shared Albums method above.

Sorry I meant to say I've been using Lightroom, NOT Lightroom classic