Cat saliva is one of the most potent allergens known to man. Allergens are substances that will trigger an overreaction of the immune system in sensitive people, resulting in symptoms of allergy and possibly asthma.
You should talk with your child's pediatrician to be sure, but it is certainly possible that the cat saliva could be triggering symptoms in your child. There could also be an issue with germs your cat may carry.
I'm sure you know this, but your baby and your cat should not be spending time in the same rooms. And I would never let your baby use a pacifier the cat has been into, without sterilizing it first.
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