CBT tends to be more symptom-based, although it's great at providing tools. You won't go much into the roots of your problem with a purely CBT therapist.

Psychoanalysis is kind of the opposite. Pretty much the main thing you do in analysis is look at the roots of issues, but you don't really get tools to help in daily life.

It sounds like you'd benefit from an eclectic approach. I've think that many psychodynamic therapists tend to take a kind of middle ground and are often trained in multiple techniques. My T, for example, is primarily psychodynamic and helps me understand why I do things or feel the way I do. Plus, he's had CBT training, so he gives me tools for specific issues when I need them.

Your best bet is to call a few of the therapists who take your insurance and ask them what kind of approach they take. Tell them what you're looking for - if they can't do it, they'll tell you.