What make you think you have a virus or worm ... are you getting any error messages and if so what are they?
You say you are getting slow download speeds ... but is your computer slow to load webpages/download emails etc.
The slow download could be the fault of the site you are downloading from.
Go to this link:
http://www.speedtest.net/
try the test 4 times .. recording your speeds each time and them post them back here.