Spaghetti Type Worms Found In My 14 Week Old Puppy Is This Normal Even If She Has Been Wormed Since Birth?

Not normal and needs to be taken care of but common. See or call your vet. If you can take a sample it may help but your description will probably do it. You may be able to just call them and pick up the correct dosage for your individual pup (s) if they have the necessary information (things like accurate weights on file). It's possible that at the last deworming they were just eggs and/or just picked up or exposure came after so wasn't effective on them and have grown. Or did you just do your 12 week shots and deworming at the vet? Be sure to clarify the next dose so the ones that are eggs now can be taken care of. If you were doing the dewormings yourself it's also possible that the dewormer wasn't effective (different parasites need different treatments) but that's the one main parasite the OTC dewormers do tend to be effective on. Not recommended to go that route since they have a tendency to be extremely dangerous and result in emergency and death even when used on label and most of the time if not used by label (so safer and often less expensive just using the vet and those dewormers as they are different). You might want to talk to your vet about dosing your other dogs JIC and if your kids are very young ( ages where they touch everything and not wash their hands and then investigate by mouth or whatever is most likely) keep an eye out but not necessarily a huge concern. Roundworms often originate from the Dam in puppies but at 3 months with several dewormings your pup may have picked them up somewhere else. It's common and pretty easy and inexpensive to take care of usually and not really a big deal unless not treated.
www.marvistavet.com
vetmedicine.about.com
www.dogfoodanalysis.com