Should I ask for a diagnosis?

I have recently begun therapy for social anxiety due to childhood trauma. I am pretty high-functioning, but I struggle in making close relationships and social interactions in many different settings. I have virtually no close friends outside of my husband and really only feel comfortable with immediate family. I'm pretty avoidant in general. This has permeated my life and held me back in so many different ways. I feel disconnected with my true self. I never realized it before, but I also suffer from anxiety.

My father was a harsh disciplinarian, control freak and not emotionally nurturing at all. He loved me in his own way, but he was not the type of parent that provided any type of emotional support whatsoever. He felt that my feelings were completely irrelevant and did not show affections in usual ways--hugs, saying "I love you", etc. In fact, I was punished/criticized for showing emotion. He fostered a feeling of shame in me and an environment where I felt completely cut off from others. Although I was whipped with a belt as punishment, I'm not sure that other people would call him "abusive", but I think he'd definitely count as oppressive. After 44 years, I'm starting to realize that his parenting was not normal and had very profound negative effects on me.

I've been going to therapy weekly and have been to three sessions so far. I have a great rapport with my therapist and I feel like I can make great progress if I keep at it.

The only thing that is nagging me is that my therapist has not provided me with a diagnosis. I've read that some therapists believe that there are downsides to providing the client with a diagnosis, and it seems that she is one of those.

On one hand, I am very curious about what diagnosis she's given me. I believe I have C-PTSD, social anxiety disorder--maybe avoidant personality disorder. But on the other hand, I'm kind of reluctant to find out, especially if she doesn't think it would benefit me at this point in time. Should I ask her if she's diagnosed me or should I just go with the flow??

Three weeks is nothing in terms of therapy. She will need to get to know you in depth probably before she tries to make any diagnosis. It took many years with my therapist before discussing a diagnosis. This was traumatic and she had bided her time before she discussing it with me.
why don't you ask her about diagnosis and she will tell you where she is with it.