I have quite severe asthma which has worsened in the last 5 years or so. I never used to be affected by it and have had asthma since I was a small child and cats from the age of 10, when I was in hospital a few years ago the doc found out I had a cat and suddenly it was like the light had come on in his eyes and he blamed my asthma on the cat and suggested I 'get rid'. I pointed out that I had a cat and asthma for the previous decade with no issues so I didn't think it was the cat affecting my asthma and I certainly wasn't going to 'get rid'!
The point of the above is that your sisters asthma may not be affected by cats, if it is then there's lots of options - tablets, 'preventer' inhalers, reliever inhalers, increase hoovering or go for laminate/wood flooring, petal cleanse etc