your experience just sounds like mine..
My daughter was officially diagnose with asthma when she is 2 years old (now 5 years old). Her asthma attack is so frequent that she was hospitalize. Sumething it all started with a running nose, cough and definitely wheezing etc.. when she is hospitalize.. the doc ask us weather we have a dog or cat at home.. which we dont.. so somehow this rumors about cat/dog fur can cause asthma attack can be true. But i know that my dear daugther has asthma due to genetic from her father (who has asthma too).
So to be on the safe side, what the doc advise us is that she go for the allergy skin prick test in the hospital. Coz asthma patient must have allergy to something. What is it..so we did just that, we sent her for the test. What they did is prick a few needle into her skin (with markings), each with a label of, dog fur, cat fur, cockroach, grass, dust and a few more. Wait for a few minute and whichever area is swollen is what she is allergy of..but lucky for my girl neither of them swell..so she is not allergy to those.. can set my mind at ease..
you might want to try that.