Medicated, is there some reason why you need to do therapy with the person the pdoc suggested? If you decided to go see a different person from the person your pdoc recommended, are you worried pdoc would not like it? You could get recommendations from other people too, as well as additional (male) names from pdoc.

I don't think you're being too picky, I just think you haven't investigated what's out there yet. You've had an initial interview with the female CBT counselor. Perhaps interview a couple of others and choose the one who is the best fit.

As for PhD vs. MSW, I would suggest visiting the therapist if they sound good in other ways, despite the degree they have, and just see how they are in person. I think sometimes the personal connection is more important than the degree. Can you work with this person? Do you connect? Also, there are more choices than PhD and MSW. (My T, for example, has an MA in Psychology.)