I didn't believe it either. If you sometimes have severe anxiety and then switch to depression, most psychs consider t hat bipolar. I am not a manic person by any means. I go from severe anxiety to just fatigue. I don't even consider it depression. The biggest thing for me is that antidepressants rarely work for my anxiety. They don't usually make me worse, they just don't work. For most people with bipolar, antidepressants alone can make them worse.
Maybe you are bipolar, maybe you are not. Bipolar is a spectrum disorder. There are many different levels. You don't have to be manic to be bipolar. I have never experienced a manic attack just that awful severe anxiety at times.
I really hope you get to feeling better soon. If you stop feeling anxious on the antidepressant alone (without the Klonopin as well) then chances are you are not bipolar. If you are taking an antidepressant with Klonopin, then the Klonopin can mask everything and make it seem you are not bipolar because when you are in an anxiety state, it can calm you down. It's horrible but a lot of time, diagnoses can be more definitely made by how one reacts to meds.
I am only speaking about the above from personal experience of myself and some experience with my friends. I also have a psychiatrist friend who talks with me a lot about these things.
I am sure your doctor is looking into everything. It's great s/he is going to check your blood prior to administration of medication. If you truly don't believe you are bipolar, perhaps you can get a second opinion.
You do sound like you have soft bipolar or bipolar II just with the little bit I read...if you go from severe anxiety to depression. You can still be adhd, like I said I am.
Good luck. Really seek out a second opinion if you are having those doubts.
I am not a psychiatrist so really don't take my word as "professional advice."