iTunes wants me to factory reset my iPad

I recently added many songs from outside iTunes to my library. (CDs, etc) I've done this many times before, and I know what I'm doing. When I was syncing my iPad Mini, I got a message saying something like "The iPad backup is corrupt. Delete the backup and re-sync." So I looked up how to delete a backup, and I deleted it. I then plugged in my iPad, and it said "iTunes cannot read the contents of the iPad. Go to the summary tab in iPad preferances and click Restore to restore this iPad to factory settings." I can't afford to reset my iPad. I use it in school, and it contains many textbooks and apps I need. Not to mention my personal apps, songs, pictures, and videos. I looked up the issue online, and found out that many issues are solved by updating iTunes. So I updated iTunes, but halfway done it seemed to freeze and stop. So I redownloaded iTunes from the website and tried to reinstall. Soon after, my iTunes.exe stopped working, and I didn't have permission to open the iTunes folders to save my library files. I gave up and went to sleep.

This morning, I did some more reserach and learned that similar issues were solved by downloading and scanning with "Malwarebytes Anti-Malware." I scanned and deleted the 40-something bad files. Apparently, my computer had some trojans and such. After restarting my computer, I installed iTunes and everything seemed to be okay. All the new songs are there, and even my playlists. So my library files weren't tampered with.

However, iTunes still wants me to reset my iPad to factory settings. I can't afford to lose all my files on it, so how do I get around this issue? Can I restore the corrupted backup and fix it, or create a new backup from my iPad so I can sync it again? I really need help, because this iPad is essential to my schoolwork! Thanks!