Alergies

So my husband has allergies to pet dander. Its worse with cats but the dogs seem to irritate it too. We own two dogs and a cat and he takes allergy pills every day, he still gets stuffed up though because he builds tolerance to medications really fast and because the carpet takes on alot of fur. Well now that I'm pregnant I'm worried that my child might take on the same allergies should I be worried? My biggist fear is SIDS of course could allergies like that be severe enough to cause that?