Could I have worms?

Recently I've been letting my (outdoor) cats stay in my room when it's extremely cold out. I've been doing this for the past two weeks. I never noticed any symptoms for worms until this afternoon when I actually found the worms in their poop. I've cleaned everything including all of my bedding as best I could and put the cats into the garage until I could get them to the vet. Is there a good chance that I have worms aswell? The worms were long and white.