Allergies

I woke up this morning with a stuffed/runny nose and scratchy eyes. Maybe it was my wife’s cat that slept on the bed with me last night. As I was trying to relieve some of the pressure in my sinuses, I started thinking about what I could be allergic to.
For some reason, I feel I know the answer to my question, but I don’t know all the details of it.

If humans can be allergic to cats and dogs, can they also be allergic to other varieties of animals such as reptiles or even other humans?
If they can, what is it that triggers the allergic reaction?

This got me thinking about food allergies as well. Are there specific things regarding food allergies that trigger the reaction, like a certain component in peanuts or seafood that makes human allergic to them?