RE: Question
NO, Avast and Windows Firewall paired with some common sense, can protect your computer without being need it to install a third party firewall.
Avast Free with windows firewall is a good combo, however adding a 3rd party firewall, like Comodo or Online Armor will also add a HIPS (Host Intrusion Prevention System) which should increase your overall system protection, and will make it easier to monitor the outgoing traffic (if you like to do this type of stuff).
Nevertheless, if you practice a safe online behavior (You can read here some good tips: http://malwaretips.com/Thread-5-easy-tips-to-avoid-infections ), you don't really need a third party firewall.
I do recommend that you start a thread in this forum: http://malwaretips.com/Forum-Security-Configuration-Wizard , so that we can give you some advice on how to improve your overall security.