The reason Helen Stoner is shivering from fear when she arrives at Sherlock Holmes office is because she is afraid for her life. Recently Helen has been asked by her step-father, Dr. Roylott, to sleep in her dead sister, Julia's room. And because of this experience, she is terrified.
"Their client, Miss Stoner, is in "a pitiable state of agitation, her face all drawn and gray, with restless, frightened eyes, like those of some hunted animal." In spite of her miserable appearance Holmes sees in her the courage to fulfill a daring plan to trap the villainous Roylott."
At night in Julia's bed, Helen hears noises, smells pipe smoke and has a sense of foreboding. She is scared that she will die suddenly just like Julia. In fact Helen is afraid of her step-father.
Helen Stoner, as she says, is shivering from fear and terror (paragraph 10 of "The Adventure of the Speckled Band").