I didn't start depth therapy until after age 50. It's wonderful.
When asked what brought me to therapy, I said that primarily I wanted to know myself better and also I wanted to feel better, I wanted my life to feel better and that anxiety and depression were issues.

I am such a loner I didn't think that I had "enough" relationships to "qualify" for therapy. I worried how I would be able to 'prove' that I should be there.

Yes, it's fine to say: These are things about me, about my life that I'm not happy with.

About the PhD.. I used to think that ONLY a PhD would do. But when I wanted to enter into depth therapy, I contacted the psychoanalytic institute nearest me and asked for a referral. My T is a LMHC and MSW. Actually, I read recently that most analysts are not PhD's.

Anyway, here's a link that might be helpful:
http://www.212analyst.org/istherapy/istherapy.html