The best thing for your baby right now is that precious breastmilk. LLL's site states:
Mothers have breastfed their babies through a variety of illnesses, from colds and infections to chronic conditions including asthma and diabetes. Your baby is exposed to any illness you have before you know you are sick. One of the beauties of human milk is that when your body makes antibodies to combat an illness, these antibodies are passed directly into your milk, giving protection and disease-fighting abilities to your baby, too.
Here is a little info on nursing a baby who has diarrehea:
Part of this article states, "Frequent and loose stools in a breastfed baby is not necessarily diarrhea. Here is more information on normal stooling patterns for breastfed babies: What Are Baby's Stools Supposed to Look Like? Diarrhea in a breastfed baby is diagnosed when a baby has 12-16 stools per day (or more often than the baby's regular stool frequency), watery stools, and an offensive odor to the stools. Just one of these symptoms does not in itself mean the baby has diarrhea.
Hope mom and baby get to feeling better soon!!