Help with iTunes! I'm desperate, please! (apps not appearing)

Hi everybody. I'm receiving my iPod touch in a couple days, and I already bought a whole bunch of paid apps on the iTunes store on my computer. They took forever to download, but they are not appearing in my apps tab. What happened, and how do I get them into my apps tab?

I am asking this because I know that whatever apps are in the apps tab will automatically sync to my iPod touch, but if they are not there, I will need to re-download all of those apps on my iPod, which will take a LOONG time.

Please help!