It's bad that I laughed when I read "She said she would rather be allergic to Josh instead of the cat, since she likes the cat better." Sometimes I feel that way about my hubby. I love my little 4 legged friends. So I did some research. This article claims to have found the cure for cat allergies. It's kind of weird I'm not sure I would do that.
This website suggests the following. http://www.catlover-giftsworld.com/cat-allergy.html
You will need to do all these things to maintain a normal life without cat allergy reactions:
Perform a daily grooming of your cat. Spend a few minutes brushing her all over (preferably outside of the house) to remove loose hair and dander (skin flakes). Morning, noon or night it doesn't matter. Just do it each day.
A weekly bath will remove much of the surface allergen, and, reduce the amount of future allergen produced, according to some studies. Use plain water, especially on older cats because if you use soap she may not stay around long enough for you to rinse her. Kittens are easier to wash this way and there's the added benefit of training her to get used to the weekly bath. Plain water is enough to capture the allergen, anyway.
There are mitts, gloves and wipes designed for any washing ritual which makes the process easier to manage than negotiating a cloth and bucket of water. Don't forget... once a week.
Though some suggest banning your cat from some or most rooms in a house as being necessary, I think this is one step short of outright throwing her out. But, I do advocate making the bedroom off-limits. Cleaning your bed coverings and sheets every time the cat has found your pillow for an afternoon siesta, or a midnight snuggle, can get old really fast. Sorry kitty. You'll have to sleep in your own bunk.
Make vacuuming a regular habit. Include upholstered furniture, rugs and carpets as well as bare floors. Tables and all polished furniture should also benefit from a regular cleaning. HEPA (High Efficiency Particulate Air) filters on vacuums and heating & cooling systems can reduce cat allergen by up to 50% in your home. Wipe the walls down with a damp cloth or sponge mop, too. Whew... I'm tired just thinking about it. But, it's really worth it!
Keep your home well ventilated and "air out" as often as possible.
If your kitty has been lying peacefully in your lap, change clothes when she is finished and put them in the laundry. Then go wash your hands, or even take a shower if you think it's necessary. It's just her way of helping you to realize how refreshing a shower can be.
Aaahhhh... the things we do for our loved ones.
Finally, if you are particularly cat allergic, wear a dust mask when performing any of the above activities.