In response to the questions you raised, yes, you can work on those with a therapist.

You can investigate different types of therapy. There is for example "Brief Therapy". CBT usually is short-term.

I suspect that this statement comes from your past, from people who were influential there: the idea that things are your fault, the idea that you are not good enough as you are, the idea that if only you got yourself to be better in some way then things would be better. The idea of self-blame.

You don't want to recount every moment of your childhood--and you don't need to--but to understand your basic perspective on yourself, a psychodynamic therapist, at least, would want you to speak to some degree about your childhood.
A therapist helped me with:

--social skills: these have a lot to do with self-image
--curiosity: curiosity has to do with self-image, with having the courage to push beyond perceived limits, with having the courage to say what one is curious about
--identify and follow passion: very much like curiosity, it takes courage and an ability to value oneself to be willing to devote oneself to a passion
--inhibition: I did not work specifically on music with my t, but we did work on inhibitions. I am now less inhibited in most if not all areas of life. If I took up my instrument again, I believe that I would play with more freedom and courage now
--appearing as a normal person: looking back, I think that I appeared as a normal person far more than I thought that I did. Being oneself, accepting oneself, makes it much easier to feel as a normal person.

I think that in discussion with a t you yourself discover how and where to drive it, you will discover solutions. My t at various times proposed different practical ideas, but that actually was getting out of her lane, you know? Her practical ideas never resonated with me. Having a person to help me discover and accept my own way, though, very much did resonate with me.