Do they think it is toxoplasmosis?
http://www.cdc.gov/toxoplasmosis/epi.htmlShe can only catch it from a cat if the cat's a hunter and kills and eats rodents that have got it already - and she comes into contact with contaminated cat faeces. People including unfortunately doctors sometimes are wrong and say that any contact with cat poo can give you it, if you get some on your hands when cleaning a litter tray. One GP once told me I may catch it from cleaning out cat pee
Anyhow there is a blood test for it - has she had that? AFAIK it's more like a virus with aches and pains and weakness, fevers etc, what you are describing does sound like an allergy or asthma type illness? (I've also heard about respiratory illness caught from birds).
If he's 19, surely he's not hunting any more? You can also catch toxo from undercooked meat. In fact most people catch it from that apparently.
Hope she feels better soon and her cat doesn't get the blame for something that's not his fault!