Cats + Baby = Allergies?

Greetings all. I hope someone can help with their own experience here...

My daughter is just over 2 months old now. I have 2 cats. About 3/4 weeks after being born she started having cold-like symptoms. I took her to the doctor when they didn't seem to be clearing on their own and she's been on a prescription for 3 weeks now.

It helped her to suffer less as it decongested most of what she had. But 3 weeks later and still symptoms?! Isn't this crazy if it were a cold? But maybe infants are sick longer? We live in an area known for many allergans.....perhaps it's mountain cedar? When DH comes home on weekends (working long distance right now) he notices a runny nose but only when home. And it's a new home mind you so I don't think there's much around here that could be causing it....But we both did have cold-like symptoms after she got them...we had them about a week later but are cleared up now.

I hear allergy testing is expensive and difficult (hard to pin-point). I can't call her doctor about it today they are closed.

Symptoms are stuffed nose, sneezing and rubbing her eyes until the skin is all red.

I feel terrible thinking it may be my furr babies. I really take pet ownership seriously and feel lousy thinking I might need to get rid of them as you tell them when you adopt them they are part of the family. But I no doubt know baby is more important.

May just be the rambling thoughts of a first time Mom here and I'm overthinking things a bit.