Hello, first of all a recommendation when upgrading or installing a new operating system to your devices, you do a backup, you are on a Mac, PC or via iCloud with this ensures your applications and more files. Having updated device will load the backup and everything will without fail.
Now to your problem is simple any applications you've purchased with id Apple can download again, as long as you're using the same id. Also check the permissions application installation it may be that you have locked (settings, app store)
Greetings.