You just being paranoid.
I think running 2 antivirus programs at once is fine in my opinion, just exclude them from scanning each other
Thank you @Anti-Malware Reviewer !Nice config, but because you are using the FREE version of avast! I recommend you install a more powerful firewall and or Zemana AntiLogger (free if you want)
I just installed Avast! and noticed they now have a "compatibility mode" for using it as a "second line of defense" - methought "Yippee!" upon reading that installed it that way. Being curious as to what the difference was I checked out the running processes and it turns out that in "compatible mode" Avast! doesn't run Real-time..