Psychiatrists diagnose those things they can help with medication. There is medication for depression and for anxiety, for example.
Therapists diagnose too, although many don't like to dwell on the diagnosis, and don't refer to it or necessarily offer a diagnosis to the patient. It is a different process and working on one area in therapy can make another area improve - for example, helping us understand what causes our depression can also reduce anxiety, as we learn new ways of thinking and doing. I might not be able to talk to authority figures, and I have a need but can't express it. I feel very anxious when that happens. Unable to express it and get what I need, I also go falling off the cliff into a depression that becomes about 'everything'. In therapy, my therapist can help me find a way to say what I need to say to get a need met with an authority figure (like work), so the depression lifts. As I continue to work on expressing what I need the anxiety that I usually feel in the beginning also is lessened. So.. would she diagnose me with depression or anxiety? Or something else that encompasses those 2 symptoms?
It is a beginning, a starting point. An exciting place in your life!
I was listening to public radio yesterday and an author who is nominated for an award was being interviewed about his book (about his dysfunctional family) and the interviewer asked if he had received therapy. He answered with an enthusiastic yes and added that he can't wait to get back into it. The interviewer said she understood that perfectly (insinuating a personal involvement with therapy herself).
So, you are in good company, wanting to feel better, wanting to know more about yourself!