In choosing a point of view, a writer is making an important decision about the impact her story will have and the way in which it will be interpreted. The choice of a first-person narrative allows for nuance in terms of the reliability of the narrator, which is very important in "The Yellow Wallpaper." Because the story is written in the first person, the narrator can only present the world as she sees and understands it; unlike an omniscient third-person narrator, she cannot tell us what is going on in other people's minds, nor can she give a definitive description of the world around her. Some stories might use a limited third-person narrator, in which the story is written from a third-person perspective (the author describing the protagonist as "he" or "she") wherein the story is similarly limited to the understanding and knowledge of the main character.
In this story, we can see from the very first sentence that a first-person perspective has been selected. The narrator refers to "myself" in the first line and, in the second line, uses the pronoun "I." The style of writing makes it clear that the narrator is describing the world from her own perspective and understanding: "I would say," "I will proudly declare."