Unfortunately, some people are very allergic to yorkies. Actually a poodle is the best dog to get if you're allergic to dogs. This is an article I found online
Allergies are not a direct result of too much hair, and even dogs with fur like human hair can cause allergies. The sebaceous glands are the culprit. Dogs, like other animals and humans, secrete an oily lubricant (sebum) through their sebaceous glands, which keeps their skin supple and their coat (hair) shiny. The allergen in the secretion causes the allergic reaction and is present in dog’s saliva and dander.
As a dog ages and the skin dries, more sebum is produced and the scaly bits of dried skin are released, resulting in dander (or dandruff in humans). It’s important to be careful when buying a puppy because you might not have an immediate allergic reaction. Puppy’s skin is supple and sebum isn’t released so they have no dander, but, you might eventually get an allergic reaction as the puppy ages and dander forms