what is an allergy anyway?

I have been allergic to cats since i was around 15 or so, when i used to spend a lot of time with my cousins. They had recently adopted a cat and i would get sneezy and had problems to breathe.
Since then, many times i have been in places where they have cats and i get sick in an hour or so and then have problems breathing, almost always including a tough night of no sleep.
Everyone knows the feeling of not being able to get enough air, at least from playing in a swimming pool.

I had opened my eyes in the middle of the night and the cat was in between both of us. I was ok. Later, once the traffic was loud and the light announced a new day, i've woken up, smiled, kissed her and then she has picked cat hair from my nose. I was ok.