There is no need to apologize for yourself. You are asking very, very good questions.
First, there are two types of bipolar disorder. Cycling between depression and “normal” is Bipolar II. People who have also had at least one episode of mania are diagnosed with bipolar I. So, if you have bipolar at all, it’s likely that it’s bpII.
However, you ask another really good question: Is it at all likely that you have been made so hypersensitive to the possibility that you have bipolar that you are mistaking normal adolescent hormonal changes and emotional growth for a disorder? I can’t answer that question on the basis of a letter. What I can do is suggest that you make an appointment with a mental health professional and take your letter with you to the first session. Your letter describes the situation very well. Asking the counselor to read it first thing will help her understand your confusion. The counselor will then be able to ask you questions that will help determine what’s going on.
I do think that settling the question will be helpful to you. You don’t want to be constantly second-guessing yourself or worrying about yourself every time you have a sad feeling. On the other hand, if you do have bipolar II, you may want to consider some treatment so that you can manage it effectively. It doesn’t have to dominate your life.
I wish you well.