Ubassoon.... I was born (or so they tell me) with severe allergies to animals. ALL animals and so as child couldn't even have a hamster or visit people with cats or dogs. I have never been within a 100 meters of a horse! My allergies manifest themselves as wheezing and eventually an asthma attack....
I went to one specialist to another and they all told me the same thing - you can never have a pet and don't even bother with shots because STILL you won't be able to have a pet. Years ago a neighbors cat started to came in to my house. I would let him out when I started to wheeze but to my delight his visits became longer and longer and my allergies less and less severe!! Well, it has been years now and he ended up living with me permanently. Eventually got another one!! (I lost them both but that's another story..)
So.. my advice to you would be - make sure you're all better and your bronchial infection is all cleared up (otherwise you'll end up with a chronic cough and shortness of breath). When you're all better - if you can get used to you kitties again slowly. Try NOT to sleep with them for a while. make sure you use your inhaler and if you can take an antihistamine or ask you doctor about Flonase.
But don't give up. I truly believe that our bodies can build up their own "immunity" to allergens.
Good luck. (I'm not sure if I was any help at all but I sympathize!)