Yes, yes, yes! Keep breastfeeding. You could pass a illness to the baby, however breastfeeding protects the baby against infection, and you should definitely continue breastfeeding in order to protect him. If he does get sick, which is possible, he is likely to get less sick than if breastfeeding had stopped. Also, if you were to stop breastfeeding you could actually decrease your milk supply or he may refuse the breast when you continue. So keep at it! Good luck. Congrats on the new baby.