Definitely bring a stool sample to the vet for analysis. I don't think tape worms wriggle...they look like grains of rice and don't move much. The vet should be able to tell what worms kitten has and the proper meds to take care of them. Most over-the-counter meds aren't very effective and some can be downright dangerous, so it's best to go through a vet for worm control.
And if you have some time to post and pictures to share, we'd love to see pics of your kitten!