When I was very young, about 10, I too had problems with kitties, dogs too.
I had the itchy problem, and got wheezy.  I also would rub my eyes, and I
would end up with a mess!
I would have to put a cold wash rag over my eyes - at least it made my eyes
feel better, and helped
with the puffiness.

We had one kitty at the time, my Mom found a good home for her...my
brothers, sister and I were so upset.
And of course the others blamed it on me.

But, years went by - and for my 14th birthday, my parents got me kitty, and
later gave my sister a kitty -
the sister to my kitty.
I did not experience any of the problems that I had - had 4 years before
that.

I have had cats, dogs, a rabbit sense then - and still no problems.
Interesting thing - my brothers and my sister, now have the problems that I
used to have.
A couple of them do have animals, but they keep them
outside, (I wish they wouldn't though).

I have recently read, that having animals around children (while they are
growing up),
actually helps these conditions, that I had as a yound child.

Not to change the subject - but in this same article, it was mentioned that
more and more
children are born with these conditions already.

In my situation, I either grew out of these conditions, or what I really
think, was being around
many animals - to this day!

Your cat does sound really cool.
Wish I could take in another right now, but my kitty hates all other
kitties!

I hope your situation works out for everyone...kitty included!!

Take care,
DJ