are there parasites in my fish tank?

Sounds like planaria or nematodes. Harmless generally towards fish - and may well get munched by them. An overload of these is a sign there's too much decaying matter in your tank. Make sure you're doing regular partial water changes and gravel vacs.

The only time I've had these appear was when a snail died. They disappeared after a water change or two. They're always in the tank, but usually in such small numbers you won't see them.