You say you are using Thunderbird to collect your webmail, so you aren't using a browser to get your webmail, so the Web Shield won't be scanning it because it isn't using the http protocol nor using port 80.
I assume you are using the thunderbird webmail extension (converts webmail to pop3 email) to collect your email ?
If so then the avast Internet mails I believe should be scanning it, I say I believe, because I don't use thunderbird.
Sorry missed the bit about you switching back to using your browser, which one, I suspect firefox ?
In which case because firefox uses extensionless browser cache you may need to have the the Scan all Files option enabled in the Web Shield, Customize, Web Scanning tab.