Internet pop ups

Hello,
I have a problem with pop ups and I don’t understand it. I had a Trojan horse thing on my laptop a few days ago and AVG seemed to sort it out as I have scanned the computer and it hasn't come up wit any new ones, but now I keep getting internet pop ups. I will be watching a DVD on the laptop and have my internet switched off and then I get these advert pop ups come up even though I haven’t touched the computer and the internet isn’t on. It happens when I'm on the internet too and I go on to sites that have never had pop ups and these new windows appear. I don’t go on sites that I am not familiar with and I don’t know what is causing these new pop ups to come up, it is worrying me as if there is a Trojan then AVG isn’t catching it and I’m not very computer savvy.
I really hope that someone can help and I'd really appreciate it too, thanks, Em