To my experience, if the bf mom gets sick, the baby can easy catch the sickness. But, it's not a bad thing as it's the time that she builds up her immune system. For the same reason, since the mom's body is producing antibiotics to fight against the diseases, the milk would contain it and pass it to the baby. Therefore, it is good to keep nursing. Just to make sure to tell the doctor that you're nursing and he may give you the medication which will not be harmful to your baby.