While the narrator might be unreliable because we must believe she is mentally ill and the events she recounts are not literally true, the author behind that narrator wants us to believe the essence of the narrator's story: that her "imprisonment" in the room reflects women's "imprisonment" in a male dominated social order. This is the irony of the story: the narrator might get the "facts" wrong in that of course there is not in reality a woman crawling behind the pattern of the wall paper, but she does hit on a figurative "truth" through her hallucinations. In her distortion of the immediate reality, we are able to gain knowledge of a greater political reality. And so, as for her reliability: no, what she reports does not literally happen, but yes, she nevertheless communicates to the audience something very true.
The narrator is a classic example of an unreliable narrator. We only 'see' the events through her writing. Some potential causes for her breakdown include her recent birth, the fact that she is not allowed to see the child, her husband's prescribed treatment of absolute rest and mental inactivity, her sister's adoption of a domesticated female (she acts as the stereotypical wife of the time - doing housework, caring for the husband and baby), the fact that her husband discourages her creativity - refusing to let her write, and the fact that she is literally being kept prisoner in the upstairs room (the bars on the windows, the bed nailed down, her husband's refusal to move her from that room). All of these could be viewed as reasons for her mental breakdown.
The narrator is considered an unreliable narrator since the story is told only from her point of view in a series of secretly written journal entries. As her mental health deteriotes so does her writing. She is considered an unreliable narrator since we only know her emotions and feelings and she suffers a mental breakdown.
We know that she has just had a baby and with today's knowledge we can assume that she is suffering from post natal depression. The treatment for such 'women's problems' is rest and no distractions. This treatment leads to her mental breakdown.