Interesting question! The beginnings of Annie John and "The Yellow Wallpaper"are similar in that both narrators begin by describing an all-consuming fixation/obsession. The heroine of "The Yellow Wallpaper" is obsessed by her debilitating illness, the "strangeness" of her summer abode, and (especially) the wallpaper in her bedroom. Nothing quite agrees with her, for she suffers from a "temporary nervous depression" and a "slight hysterical tendency."
The narrator is frustrated that her husband has shown little sympathy for her suffering. She finds that she is constantly irritated with him, and she privately faults him for her unhappiness. Similarly in Annie John, its namesake narrator harbors a personal obsession: she is fascinated by death, largely because she is afraid of the dead. Annie John must hide her fixation with death from her mother, whom she enjoys an especially close relationship with. In fact, Annie John's obsession with death is so all-consuming that it colors all of her experiences in the first chapter.
This is similar to how the story begins in "The Yellow Wallpaper." The narrator is so fixated on her malaise that it colors how she relates to others (especially her husband) and how she perceives the events of her daily life. Even the wallpaper distresses her: it is a "revolting . . . unclean yellow" in places and, by variation, a "lurid orange" or "sickly sulphur tint" in others. The descriptive language points to disorder, decay, and neglect. The narrator is expressing her sense of being marginalized and forgotten.
She must even hide her love of journaling from her husband. However, she is not an entirely reliable narrator: her analysis of her situation is deeply colored by her frustration and dissatisfaction with life.
Another similarity also lies in how both narrators perceive their fears. The narrator in "The Yellow Wallpaper" becomes so fixated by the wallpaper that she imagines she sees a "strange, provoking, formless sort of figure" among the patterns. The figure purportedly has a pair of "bulbous eyes" that constantly monitors her movements. Meanwhile, in Annie John, the narrator fears that the dead will haunt her until she joins them in death. So, both narrators believe that they are being stalked by elusive figures that seek their eventual destruction.
As for differences, the narrator in Annie John is a young girl, while the narrator in "The Yellow Wallpaper" is a grown, married woman. Another difference is quite stark: the narrator in "The Yellow Wallpaper" finds little to praise in her relationships and so remains emotionally detached from her loved ones. Her husband is "careful and loving" but too "clinical" and fastidious for her wishes. Meanwhile, her infant is a "dear baby," but he aggravates her nervousness. On the other hand, the narrator in Annie John experiences a definitive separation from various acquaintances and loved ones through her imagined death.
As for endings, the one great difference is that Annie John ends with the narrator beginning a new life, apart from her mother (and the rest of her family). She travels to England to begin her nursing studies. By the end of the story, Annie wants to differentiate from her parents; she desires to develop and define her own identity. By going to England, she is seen as taking charge of her future. Meanwhile, the narrator in "The Yellow Wallpaper" loses her grasp on reality altogether: gripped in the throes of insanity, she becomes a prisoner of the ailment that has long tormented her.
As for topic sentences, they are used to express specific ideas. As you know, a topic sentence can be found at the beginning of a paragraph: it tells us what the paragraph will discuss. So, a topic sentence reveals the main idea behind the paragraph. These main ideas must, of course, support your thesis statement. So, first, you will have to decide what your thesis will be. Will you discuss mother–daughter conflict, gender roles, or female agency?
Here's an example of a topic sentence based on the theme of female agency:
The narrators achieve diametrically opposed results in their quest for identity: one manages to embark on a journey of discovery, while the other languishes in the realm of madness.