We have three dogs, I have severe dog allergies. I also foster on occasion. When we got our first dog he was a Shih Tzu since they are low shed. I had a reaction to him for the first few weeks but with time, he doesn't bother me anymore and actually sleeps on my pillow with me. I've built a tolerance to MY dogs. I still react to my cousin's poodle.
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Ahhhh - I thought I was the only one who liked to torture herself, here. LOL!
I am allergic to all animals. I grew up with cats, and those are actually the worst for me now, IMO. They start my asthma up.
Dogs give me runny nose and (recently with Baby Hazel we just got) Hives. Wherever she touches me - Hive-O-Rama!!
Just as Aimee mentioned, I also built up a tolerance to Charley and assume the same will happen with Hazel....and as soon as baby girl gets her spay stitches out, a good bath will help her too.
So - for now. I cover from head to toe. Long Yoga Pants and a long Yoga shirt (cuz she likes to snuggle - I cannot deny her this!!!

) and I know eventually I'll be fine around her.
Until then...Zyrtec, Calamine Lotion, and Benadryl cream.
All that being said - I couldn't tolerate the breathing thing. That would be a no, for me.

I love cats. LOVE THEM. Cannot have them.