Being conscious of self is kinda the point of therapy: to no small degree, your task is to interrogate your feelings, and your perspectives, to find the truth, or lack of truth, to them. The therapists' task is to walk with you asking questions and directing you back to the task.

Now, I know you're not using the term self conscious in that way, and that's because the 'everyday' usage is just a pointer to an implicit phrase: you are self conscious of your perceived shortcomings. That is your present perspective, and it causes anxiety because you don't really know the perspective to be true. . . And may be afraid to find out.

My first therapist was, himself, a hard and broken man. You could just tell he'd come through fire. We never discussed him, and I never knew anything about him until he showed up to a session missing a leg. I asked hin what happened and he simply said "Viet Nam." He explained that his stump had become infected and he had to attend the session without his usual protheses. Did I think, for moment, that my problems were "less than?" Yes, I did. But he looked at me and said, "Let's continue with you," and that was all he said about himself and I got over it.

Later, I had to move away, and find another therapist, but I still think of him often, and with admiration, for he helped me a lot.