Is breastfeeding baby safe when you're vomiting
Illnesses or food poisoning that causes gastrointestinal symptoms like vomiting, diarrhea, or stomach cramps are safe to breastfeed through because those illnesses and viruses do not enter mom's bloodstream and therefore does not enter breast milk.
If you are sick, the best thing you can do for your baby is continue to nurse. When you are sick, odds are your baby has also been exposed to what made you sick, and baby needs to nurse to receive the antibodies that your sick body is already producing. These antibodies will either protect baby from getting sick, or at least help baby not to get as sick as you are.
It is very rare to need to stop breastfeeding for illness. To quote Dr. Ruth Lawrence (as cited in an article on KellyMom), “HIV and HTLV-1 are the only infectious diseases that are considered absolute contraindications to breastfeeding in developed countries."