Backup Your Mac
Backup your Mac before you install the macOS Catalina update. There is no reason that you should not at least back up your important files to the cloud and at best have a local Time Machine Backup handy.
This is important even if you are already on macOS Catalina and simply installing the 10.15.3 update.
If you run into any problems installing macOS Catalina, you can restore from a backup and be up and running on macOS Mojave in no time. From there you can try installing macOS Catalina again or figure out what the problem is.
At the very least we recommend checking your Time Machine Backup, making sure important files and all of your photos are backed up. This can be in iCloud or another service, just make sure you have a backup.