Hi I.,
Allergies can be a tricky thing. His asthma can be induced by environmental as well as chemical triggers in the home. Aside from the cat dander, chemicals in carpet shampoo or cleaners can really effect the respiratory system.
I started shopping at Melaleuca as a safer alternative for my family. It may be something for you do look into for yours. They have much safer products, free of harmful chemicals that contribute to cancer, eczema, allergies and asthma. They have an awesome product called SoluMel that kills dust mites and pet dander and can even be used as a carpet cleaner, sprayed directly or in the shampooer.
I love that I found this store. I feel so much better about what I use in my home and it saves us money over the major brands we used to buy. If you're interested; check out their website at www.melaleuca.com.
P.S. They're a membership store like Sams or CostCo, but if you want to check it out, the yearly membership is reduced to $1 right now until July 20th, instead of the normal $29.
Good luck. I hope you find the solution for your family and some safer alternatives that can take that load off his immune system!
Have a blessed day!
T. S.