My 7 yrs old daughter has mild bronchitis, is it due to our kitten?

We just got our 2 kittens 4 months ago, they r 6 months old now. My daughter has been coughing for over a week now, and the Dr said that she has bronchitis and this might be due to the kittens' fur (but they dont sleep with her or go to her room), and he advised us to get rid of the kittens as they might even give my daughter asthma in the future (my family got no history of asthma) . Is it true she'll develope asthma just because of the cats in the house.