What anti-spyware programs do you have?
When you call Ad-Aware anti-spyware that is not strictly true. It is an anti-Adware program, to stop adware installing on your computer. But that's me just being niggling. We all call these pests viruses, spyware and the like.
The only program I know that can "infect" your computer from spyware before it gets in is SpywareBlaster from http://www.javacoolsoftware.com/
It immunises your computer by ;
Prevent the installation of ActiveX-based spyware, adware, browser hijackers, dialers, and other potentially unwanted pests.
Block spyware/tracking cookies in Internet Explorer and Mozilla/Firefox.
Restrict the actions of potentially dangerous sites in Internet Explorer.
But it won't catch "all" spyware. You generally need a suite of applications, and most of them, other that SpywareBlaster, you have to do a regular scan of your system.
As suggested, you "could" change your browser to a more secure one, but that won't prevent infected files from being introduced to your computer from downloads, infected CD's from friends, etc, or email attachments. You need to stay on alert, and scan regularly.
You didn't say if you have an Anti-Virus program, or a Firewall. Both are essential.
Mark