Spyware Worries

I apologize for not knowing much about this.

My computer's been slowing down so someone suggested downloading Ad-Aware and checking for spyware. I just ran a scan and it came up with 53 spyware items, 11 from Alexa and 42 tracking cookies. Six of the tracking cookies are in the my documents and settings section. The computer has Windows XP home edition on it.

I asked about spyware removers at work. People were telling me that they often pick up things that aren't actually spyware and if you delete them you can end up deleting files that you need.

I'm taking classes on line and don't know whether or not some of these spyware items might have been put on the computer by the school. Their web site does keep track of what I have and haven't read, which pages were visited, and the number of times they were accessed. If they put any spyware items on the computer I wouldn't want to remove them.

How bad is spyware and what is a normal amount of cookies? What can or should I delete? How can you tell who put them on there? Any advice from patient computer experts is greatly appreciated.

Thanks!