There are a couple of different types of conflict going on in the story. I believe that the primary conflict is Man vs. Society. The protagonist is living in a society (and further, a home) where she is not treated as an individual. She is controlled by both her brother and her husband as they attempt to do what they believe is best for her as a sick woman. They do this without any real consideration paid to what she wants. They force her to accept the idea that her own thoughts do not represent reality and that the only opinions that can be trusted are those of the men who are caring for her, regardless of what she wants or how she feels. TheMan vs. Self conflct stems from the Man vs. Society conflict. As society is telling her that she is crazy, cannot trust her own thoughts, and must give complete control in her life over to the men, she struggles to maintain her sanity and determine for herself what is real. She becomes increasingly aware of her powerlessness and, as she tries to repress this newfound awareness, she descends further.
The main conflict could be classified as "Man vs. Himself", if you were to use common terms. The main character struggles with herself, although the conflict is not referred to directly; her struggle is with her descent into madness. It is important to note, however, that there are other conflicts in the story that contribute to the main conflict, such as the main character's struggle with her husband and others she finds controlling and her conflict with her environment.
The conflict in the yellow wallpaper is an internal one between the narrator and herself. her husband thought she was crazy so he left her locked in a room. The conflict she suffers is trying to keep herself from going completely insane. she starts to see the yellow wallpaper as prison bars and starts to people crawling behind it. She slowly succumbs to the insanity and so insane.