Hello - Yes she could very well have parasites. The cycle of itching could be from the cycle of the parasites reproducing. Pinworms are very common in small children - the females come out at night and lay their eggs on the anus - this causes itching. They will go back inside the body until it is time to come back out and lay eggs again.
This may or may not be what she has, but it is well worth looking into. Many parents find that hiding pills in applesauce, pudding or jelly (thanks to mollybloom for this one) does the trick. One can also put powder herbs into molasses or jelly and have the child swallow the medicine along with the treat.