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By “killing” Avast, you have no antivirus protection unless you have something else installed in the meantime. I think your problem was your firewall settings, not Avast.
When you installed Comodo, did you disable the AV portion?
Did you put Comodo as an exclusion in Avast under Settings and Real-time shields > Expert Settings? These are just a few troubleshooting things we could have worked with you prior to you uninstalling to help you. Now without AV protection, you are swimming with sharks.
BTW, Norton leaves many remnants behind, so if you do install it and decide to come back to Avast, you need to uninstall via the vendor’s instructions then reboot. I also recommend that you search in Safe Mode for remnants as well, and use a system cleaner afterwards (like CCleaner).
By doing “routine malware checks,” I’m assuming you are checking with an on-demand scanner for malware. Remember Avast is resident protection and will prevent malware from getting into your machine while the on-demand scanners allow the infections to get in your machine and then remove them later. On-demand scanning compliment resident scanners, but are no substitution.
Please let us know if you have questions so that we can assist you further so that you are protected. Thank you.