I am a graduate student in English working on my final paper for a class. I was assigned a particular author to write on, but about halfway through the semester another student wanted to write on that author so I agreed to write on a different author. I had already read some articles on this second author so I thought I would be able to come up with a good paper topic. I thought I had come up with a good idea for a thesis, but as I did my research, I found that my thesis contained essentially the same idea as a supporting argument expressed in one of the articles I had read. I expressed my concern to my professor as I began working on my paper; he read the first few pages and said he did not see a problem. I have cited the author's statements and ideas that I feel coincide with mine, but I still have a troubled conscience -- I feel that my ideas are not sufficiently my own and that my thesis is far too similar to the arguments in this article. It is too late for me to start on another paper, but I'm not sure that I can in good conscience turn in this paper. If anyone has any advice, I would appreciate it.
From your description, it doesn't sound like a question of plagiarism (you say you're referencing the relevant paper, and I assume you're either paraphrasing it or using quotation marks as appropriate), but a possible lack of novelty. Lack of novelty is more of an issue when you're trying to publish in a journal or present at a conference. Usually class assignments don't have to be novel; they just have to reflect your own work. If your professor is satisfied, I don't think you have a problem. I would do my best to extend the ideas from the other paper, i.e. add something to their analysis.
I think your concern reflects well on you (as does agreeing to let someone else take your first choice), but the way I read your question is that (1) you formed an opinion what to write, then (2) discovered in other secondary literature that someone else agrees with you, and had already made supporting arguments similar to yours.
That's not plagiarism. It just means that your work is less novel than you'd probably hoped. As your professor considers it adequate for purposes of your class, you should be fine.
I'd shy away from reading more of that source though to make it less likely to be subconsciously influenced by their reasoning.
I know this paper probably does not have the rigor of an academic journal publication but in many disciplines it is common to include a section reviewing relevant publications and how they relate to your work.
Perhaps you could include a small section in your paper reviewing other papers and highlighting the difference between those papers and yours (even if the differences may be small) or how your work builds and improves upon the other papers.