We have 2 dogs and 4 cats. One of our dogs, the lab mix, sheds more than all 4 cats put together. She also barks at anything that walks by our house, which some people would find very annoying (most of my family, for example). The other dog fumigates our house at about this time every evening.

They poop in the backyard, which is pretty disgusting, especially when stepped in.

But we put up with these negatives because they are great pets and there are lots of positives to having them.
Same with the cats. Yeah, scooping the litterbox is not fun, but we bought one of the fancy scooping litterboxes and we only have to scoop one of the boxes. There's not much of an odor, unless they've just used the box. Oust spray is our friend.
Oh, and 2 of my kids (teens) say that they only want cats when they are older and not dogs because dogs are noisy and too demanding. They like the type of interactions that they have with the cats and are much closer to them. Of course they will possibly change their minds, but right now they are very verbal in their thoughts.
Being allergic is no fun. Chocolate gives me migraines and because of that I don't like it as much as I used to. I don't knock it to people who do like it and sometimes I even have a little, but I know when to stop to avoid a bad headache. I can understand why you wouldn't want to be around a cat if you're allergic and can see why you associate feeling bad with cats, but assuming that you're an adult, you should have the reasoning abilities to move past the hating of an animal.
I'm not a big fish or bird lover. Have no desire to have either as pets, but I think that they are both pretty cool and I can sure admire the ones that belong to someone else without wanting them myself.