I do not recommend anti parasitics,not even the naturals while breast feeding. Everything goes into your milk. On the other hand, babies get infected with whatever you have in utero and via breastmilk too. You willneed to deworm your baby once older. (cannot really know what is the safe age)
Look on this website where there are so many tips on treating small kids:
debugyourhealth.com
your description of flat pieces sounds like a tapeworm. what your oldest describes by pasta/spaghetti is a roundworm.