R.R.
Hello R.,
My name is R. as well... spelled same way LOL.
I have a 5 yr old daughter and we had a similar situation. Her going back and forth when her father and I were split up
was very hard. She had puffy eyes all the time. I had a cat at my house as do you. I've had the cat my daughters whole life. However, children are not always born with allergic reactions they develop them over time. You really should go to a pediatric and see if it's the cat first. Doesn't mean you will have to get rid of cat, they have medication you can give baby to keep cat. Also the transition is hard from house to house for her, if you and dad can make her bed at both homes similar... same type of pillow, same sheets, same night time baby, it will ease her discomfort. Try Synthetic sheets nothing with feathers. Does dad have pets? Also cleaning the air filter in both homes is an easy thing to do that can also make a big difference and should be done every 4-6 months depending on the season. With my daughter it was a mixture of all of it. I wish you the best of luck. Let me know how it goes.
R. Romero