Newborns do like to nurse often. My babies would nurse every 2 hours sometimes more sometimes less. They have very small stomaches and breastmilk digest easily(which is a good thing). Is your babies taking pancreatic enzymes? Another reason newborns nurse often is to stimulate the mother's milk. The more they nurse, the more milk that is produced.
So, to make sure you are making enough milk; drink lots and lots of water. Eat healthy, oatmeal is supposed to boost milk supply; I would eat a bowl every day for breakfast. Rest, reduce stress. Take your prenatal vitamins.
Have you seen a lactation consultant to make sure you baby's latch is ok? I'm not sure what a breast sheld is or the purpose of it.
That said; having a newborn with CF and breastfeeding is stressful.. I think my daughter with CF nursed more often and less efficient than my son without CF. She just plain needed the comfort and calories.
As the baby grows and their stomaches grow they won't need to nurse every minute of every day.
Are you burping the baby after nursing? Could she have a little reflux as well?
REbecca