Last question first, I kept all of the HW herbs in glass jars in the fridge after I got them. I did that so as to keep them as fresh as possible. It's encouraged by Humaworm to freeze herbs that you don't plan to use for a while to keep their viability, and I do that with my home dried herbs like oregano, so I'm certain it's ok to refrigerate it as well.
I'm so sorry your kids are having headaches. I did as well on my second round of Humaworm. May I ask, what does "run lines" on your children's faces mean? I'm from the Northeast, and we probably have different verbage than the rest of the country! Also, how old are your kids? I had my boys take it two weeks into my treatment when I realized that we may all have ascaris, so my older boy did the adult version, and my 12 year old did the children's because he was borderline big enough. No one, except for myself, showed visual evidence of worms, so I may have been the only one after all. I guess that's it for questions for now, but I hope it gets better!