As you investigate what you are and question the personal identity, you may find, even at an early stage, that you become less self-conscious.
One dictionary definition of self-conscious is: "unduly conscious of yourself as an object of notice." That is the way I am using the term here.
I began noticing this in everyday interactions, such as when standing on line at the check-out counter of the supermarket. Prior to self-inquiry, I'd have an awareness of how I was standing on the line, such as the position of my arms and hands. I might also think about whether my hair (or should I say what is left of it) was out of place.
These are subtle things, but there was some pre-occupation with how this self was presenting itself to others. It's a slight undercurrent of being ill at ease. My guess is that you've had this feeling at some point in your life.
After months of inquiry, this pre-occupation diminished considerably. There was little attention given to the positioning of the arms, or what I looked like in that particular moment. Nor was I concerned with how the cashier or others on the line looked or acted. It felt more like being part of the space, as opposed to being an individual object in the space.
Becoming less self-conscious is not to be equated with gaining confidence. During self-inquiry, you will usually have moments of feeling lost, which most people would describe as a loss of confidence. As I see it, building confidence is the game of the separate self. It is a judgment made by the separate individual by comparing its level of confidence with the confidence level of others.
Attempts to build confidence strengthen the separate self. Nondual investigation leads to the dissolution of the sense of the separate self. If there is no separate self, what entity needs to build confidence? Only the ego or separate entity would be concerned with building confidence. I played that game for decades until I realized it was a dead end.
As self-consciousness diminishes during inquiry, the concept of the separate self is eroding, but there is fear and uncertainty as to what will emerge or take the place of the old concept of self.
Nothing to worry about. Let it unfold. Take it as a good sign if you find yourself becoming less self-conscious.