I am allergic to dogs and cats (surprisingly, not the rabbits) and everyone here knows I will not give up Phoebe, Lucy, Mao or Eddy (the cats). But, I am used to my own cats and don't have any trouble until I come into contact with another cat. My doctor also told me that he would not dream of telling me to giving up my animals since most people will change their doctor before getting new homes for their pets. But, he did give me some information on how to manage the asthma and allergies. Number one on the list was to regularly groom and brush the cat. My cats don't mind this because it's attention and another form of petting to them. Beaver (rest his soul) loved grooming time so much that all I had to do was tap the brush on the grooming table and he was up in a flash.
Number two was remove the carpets. Well, just so happened I did not like the ugly brown carpets that were in this house anyway. When I did remove them and saw the INCH of dirt that was underneath, I was horrified! I put on a mask and cleaned it up and that took a long time.
Dusting regularly is also key. That one I'm not so good at, unless you call dusting whenever I cannot stand it any longer regular.
I had the vents cleaned and they were gross! Maintaining them now that they have been cleaned is a lot cheaper.
So there are a multitude of ways of controlling your asthma and allergies without resorting to giving up your companion.
Good luck,
Katherine