M.B.
As others have noted, if your friend is that allergic, it really doesn't make sense that she would even consider staying in a home that has a cat. So, I would also suggest a hotel or perhaps a neighbor with a spare room and then perhaps you can visit outside (if the weather stays nice). Honestly, do you really want to take the risk that you might be calling 911? The allergy medicines just can't cover a situation like this when the allergy is severe and again, I can't fathom that someone that is severely allergic would potentially subject themselves to such a reaction.
Just as an example, we do not let our cats in the bedrooms. My son had a sleepover and of course, I always ask ahead of time if kids are allergic. We had one boy who said, no he wasn't allergic, but his dad was. By the time, he left our house the next day, he was sneezing and eyes were swollen and all that kid did was sit in an upholstered chair for about 15 minutes - other than that the kids were outside or in my son's room.
So, even if you try to clean, it's just not possible to get everything out of upholstered furniture or ANY permeable item - drapes, books, all your family's clothing, linens in the bathroom, etc.