It sounds like the fear is a fear of making a fool out of yourself. What does that mean to you? How would that work?

In a situation where you conclude that you've made a fool out of yourself, is that judgement coming from others or from yourself?

We all blunder sometimes socially. I would guess that most of the time what we are thinking of as something that makes us look bad is not even noticed by others. We judge and shame ourselves and the blushing comes from the shame.

I had a problem with blushing because I felt guilty. As long as I can remember. In school, if the teacher talked to the entire class about an issue, I felt like it was really all about me and the teacher was, for some reason, just not singling me out. Later in life, on jobs, when a department was receiving criticism or being blamed for something, I was likely to blush because I was so programmed to feel guilty that I reacted as if I was the guilty party. At that point I was in therapy so I was able to talk to my therapist about it. We spent some time practicing differentiating between feeling guilty and being guilty, between shame of 'being' that was part of my growing up and shame inflicted on myself through the internalized parent. When I was made aware of how this worked, it took some practicing but eventually it became something I could stop if it began, that I was in control of stopping because I was in control of it starting in the first place.
It rarely happens now, so I guess the reprogramming was successful.