Oh, but there are so many great conflicts! Let's look at three of them distinctly - the idea of what's "main" really is going to have to come from you.
Person vs. Society: In the Victorian era, when this short story is set, the understanding of mental illness was extremely limited. What is most likely, from the contextual clues given by the narration, is that the narrator is suffering from Postpartum Depression, or depression that specifically afflicts mothers who have recently given birth. They very often feel overwhelmed, unprepared, unattached to their infants, confused, irritated, detached, or any number of symptoms. However, at this point in time, PPD was not an available diagnosis. As a result, the narrator is prescribed the best possible option for the time: rest and solitude. Today, we know that this is the worst possible treatment for depression. However, for the time, it was the only treatment. The narrator is in conflict with the beliefs and practices of society.
Person vs. Person: John, the narrator's husband, is a member of this same society. As a result, he believes that he is acting in his wife's best interest by keeping her safe (read: isolated). Any time she tries to explain herself or in some way disagree with him, her actions and statements can easily be attributed to her mental illness. The narrator is in conflict with the well-meaning actions of her suffocating husband.
Person vs. Self: The narrator herself is suffering from a break in reality, most likely instituted by PPD and exacerbated by extreme isolation. As a result, she is struggling with the reality that her senses present to her, which she simultaneously recognizes as true and false. The narrator is in conflict with herself, whom she no longer can trust.