A lot of good advice from the many wise mommas below, I hope you take to heart that everyone has your & your daughter's best interest at heart.
I want to address your comment "we will do another treatment in a week or two". One week or two weeks is a big difference when it comes to treatments for things like worm & bug infestations. The reason is that these critters have a specific life-cycle, and the medication that you use to treat them usually targets them at one or two specific points in that life-cycle.
So if you treat now, & it only kills fully mature adult worms, but not the eggs or larvae that might be in the system, treating tomorrow will not do any good, because those eggs & larvae haven't had a chance to mature into adult worms & be affected by the medication. (this is an example, I am not knowledgable on the specific life-cycle of the pinworm).
Please, check the instructions on the medication carefully, and follow up with the pharmacist you spoke to previously, to make sure you give the 2nd dose at the appropriate time. Worming medications are relatively safe (esp OTC products) but you will want to minimize your exposure unnecessarily.
Regarding the diagnosis & treatment of the worms - most worms are pretty specific (this applies to humans & pets like dogs & cats), and will often present in specific ways. Given that you had the worm present to identify, & you consulted with a health professional, I think its fine to treat OTC, knowing that if it doesn't resolve the problem, either a 2nd treatment will be needed, or a follow up with your doctor. I did find information that there is a prescription medication, albenzadole, which appears to still be available.
Most importantly, avoid cyclical reinfection - make sure to take all the necessary steps to cleaning your home thoroughly, & maintain proper hygiene for yourself & your daughter. Hopefully this will be resolved soon! Good luck. T. :)