You absolutely should have a firewall active; it is the primary filter for what your computer is exposed to on the web (after a hardware router, if connected.)
The Windows firewall does a fine job of inbound protection, but has very little outbound control, which may be important. Certainly worth investigating if you want to use a two way firewall, like the one mentioned above.
Avast is an antivirus. It does (IMO) a fine job of filtering what you then might choose to connect to, that may have been compromised.