I think you are on the right track. The emotional effect Poe intends to create in the reader surpasses the frightening, however, and would be interpreted more accurately as one of horror--the strongest emotional response to the unimaginable. Does he achieve horror in the reader? I would say so! Much of the story's power, with its final horrible revelation, is created as the story develops step-by-step through, as you said, mysterious details. The mystery is resolved and the horror is achieved when the Red Death actually appears inside Prospero's castle.
So why is this such a scene of horror? Examine the story for details that establish how horribly people suffer when they die from the Red Death; these are found in the beginning of the story. Examine the great lengths Prospero goes to to escape from the Red Death. Examine Poe's description of the mysterious guest when he suddenly appears among them. His "costume" is pretty shocking and revolting! Finally, establish the people's horror when they attack the masked figure and realize it is not human. The concluding passage in the story emphasizes the horror that has occurred within Prospero's castle. Good luck with your essay!