EDIT: Okay, so after I just turned on my computer and after I logged in I saw the "Radeon Update & Install" screen. I wanted to try installing the driver update without using DDU just to see what would happen and I was able to install the 2019 update without any problems. After my computer restarted, I noticed that the Radeon Settings was still pinned to my task bar. I opened it expecting to get the "Radeon Settings and Driver versions don't match" message, but it opened without the message popping up and Radeon ReLive was installed.
I'm guessing that if you use DDU before updating you're going to run into the Radeon Settings and Driver versions not matching and Radeon ReLive not installing. So, just keep the previous driver installed while you do the update. Like I said I'm only guessing since it worked like this for me.
As I stated in my main post, the driver I was previously using was 18.12.1 and since 18.12.2 was giving me problems after using DDU I rolled back.