Cats are killer for me too, also feathers, dogs, house dust, tree pollen, grass, etc. I was told by the asthma clinic to stay away from my friends cats and right enough it only gets bad in that environment. If you can`t part with your treasured pussy, do try to keep it out your bedroom as thats where it will probably be worse with he/she lying on your bed.
Ask your GP if you can try Seretide if you`re not already on it. If I get a bad attack during the night I use that and get a great sleep right through till morning. I think it last for up to 8 hours. Also ask for a skin allergy test.