It kind of defeats the purpose of having the AV if you don't let it tell you what it is doing. There are many viruses that can't be removed by AVG and if that happened, you wouldn't be notified if there were no popups and the virus might destroy your installation. The popups are there for a reason. So you need to get rid of the cause of the popups. If they keep coming back, then the virus is still on your machine.
Try running a scan with AVG in Safe Mode. Try another scanner, like the online Trend-Micro scanner. Scan with other anti-malware apps, too, that may be better at identifying threats that are not viral.
Free anti-malware scanners:
MalwareBytes trial A-Squared PrevX CSI Free Version Spybot S&D RunScanner Ad-Aware 2007 SuperAntiSpyware Spyware Eliminator Emco Malware Destroyer Spyware Doctor Arovax Anti-spyware Trend-Micro Rootkit Buster F-Secure Blacklight Bootzilla (Bootable anti-malware CD with many other tools.)
List of freeware security software