I asked Avast about this problem, but since they don't provide support to free users I have to post this here.
So, here's what I originally said:
"I had Sophos Home for Mac up until I heard about your antivirus and saw what it was like, then instantly dumped and uninstalled Sophos, then I tried to install Avast Mac Security until I was met with an error saying that Avast was incompatible with Sophos and since I had it, Avast couldn't be installed, even though there are no traces at all that it even existed on my Mac. Please help."
By the way, I used the bundled uninstaller, I didn't just drag it to the trash.