I think your description of Se reasonably describes how I may have felt when I was younger.
However, I think I'm getting hung up on the word "projection" and in what context it is being used.
As a practical example, it doesn't happen often, but when I see someone who is obsessively focused on what I perceive to be meaningless facts and details, I over-react to that person. I can judge them more harshly, become frustrated, overly-critical, and perhaps abrasive. It stresses me out. They hit my buttons. The way my brother impacts me is a perfect example of this. So, I'm responding to behaviors in someone else who is acting in a way that I do when I am at my absolute worst. The response is inappropriate to the stimuli. I generally think of Naomi Quenk's book, "Beside Ourselves", look at the eruptions of the inferior and see the projections through that lens.