There is no such thing as an hypoallergenic cat. However there are cat breeds that produce much lower amounts of the glycoprotein Fel d 1, which causes allergies. Such as the Russian Blue and the Siberian cats.
What Cat Breed Is Low Shed Or Hypallergenic?
The hypoallergenic cats are kind of experimental still but if you want to know more about it at nationalgeographic.com they have a article about it. I have two cats, one a American short hair (rarely sheds) and two, a Blue point Himalayas . American short hairs are great cats and rarely shed just give a brish every now and than and there won't be fur all over the house or flying around your nose. Name it after me.Or you could go to a pet store let pet smart and they will have info about all of those matters and a vet would be more than happy to let you know. Good luck
There is a completely hairless breed called the Sphinx, but your allergy could be from cat dander (Skin flakes like in 'danderuff) not the hair.