I am writing a response paper. This is the last three sentences in my introduction paragraph. Charlotte Perkins Gilman has created a character that believes she is trapped within the yellow wallpaper. The yellow wallpaper that the narrator begins to detest is a significant symbol in the story of the narrator’s declining mental state. Her mental instability is shown in the way she describes the yellow wallpaper and how this description evolves throughout the story. Do I have a clear thesis? My effective response paper needs a clearly defined thesis that will answer the "so what?" question and reveal something about the subject

Your thesis, the last sentence of the paragraph, is somewhat clear, but I think you could make it even more so.  First, the narrator does not believe that she is trapped in the wallpaper until the very end of the story; she works to strip the paper, near the end, in order to help the "woman in the paper" get out. She only believes herself to be that woman once she has "liberated" her by stripping away enough of the paper.  
Next, the narrator only "detests" the wallpaper in the beginning of the story.  Soon after, her opinions begin to change, and she comes to believe that she might actually be getting better because of the paper (although we know she is not actually getting better, but worse).  Later, though, she seems to think of the paper as bars which imprison another woman.
Finally, you are absolutely correct that the narrator's declining mental stability is related to her descriptions of the paper.  However, I think your thesis should include language to this effect: it is not just her "mental instability"—some consistent condition that does not change throughout the story—it is her increasing instability that is reflected in her descriptions of the paper.  I think you could also be more specific about how her descriptions "evolve" in the story: does she begin to hate the paper more?  Does she begin to like it more?  Does she attribute life to it, or does she think of it as a cage?  
Your thesis could read, for example, "The narrator's increasing mental instability and eventual identification with the woman within the wallpaper is conveyed by her evolving descriptions of it: first she __________, then she __________, and finally she _____________."  Such a format would give you reader a clearer idea of how you plan to argue your point.  It would also give you a nice "map" to follow as you construct your body paragraphs: one for each of the blanks above.