You can consider copying the user folder to a new OS installation or to a working Mac with a similar OS version. Target disk mode will help with that.
That will migrate the data, if you create a new user in Users & groups with the same 'short name' a.k.a. 'account name' as the folder. Then you may be able to login & access all the content for that user.
Your post is a little vague as to what you are trying to achieve & what errors you have seen. It's also possible you may be using server based accounts, which is not uncommon in larger education environments. If you want to attempt other methods please explain more about what you see, you shouldn't have to lose data unless the disk is beyond recovery or your home folder is encrypted.
For Adobe, see if you have any way to contact them. They may be able to supply SN's if you have setup online accounts with them, I suspect they are all somewhere within their web interface for the schools account - if you can figure out what email was used for login.