no idea about being allergic to animals (thankfully, i'm not myself) but i do foster for a rescue group in melbourne, and i was lucky enough to foster 2 Cornish Rex's.
Any of the Rex breeds (and a few other specific breeds, Abyssinian etc) are considered "hypo-allergenic", due to their fur.
They've only got the dander, not the hair like standard cats have (making them ridiculously soft!!)

Its actually the saliva that contains the allergen, and because cats lick themselves and shed the hair, people are convinced its the hair that makes them allergic. So the Rex breeds are wonderful as they have little fur to shed, and its more like soft wool type fluff. I love it - and perfect to snuggle with on a cold night
Anyway, the moral of this story if you still want a furry friend, have a look into one of the Rex breeds.
They can be stupidly expensive, but if you go to shelters or rescue groups they may have a couple in care (we still have one in care right now).