I don't think anyone is doubting you writing the paper. The comment about plagiarism was meant to be a light-hearted joke. Teachers can use computer programs to search the interweb for similarly worded articles/publications to see if a student just copied something someone else wrote. The joke being that if a teacher did now, it might return a result since you posted it here. In essence, it would be saying you plagiarized yourself. Obviously not something you'd run into since you're homeschooled.
Don't sweat it. And nice job on it!