Many psychologists/psychiatrists have taken up this question of the "me" and the "not-me" and the sense of boundaries that are akin to this seeking identity business.
RD Laing, radical psychiatrist in the 1960s, and '70s, who I met once at a workshop he gave on schizophrenia. He wrote two books - "The Divided Self" on psychosis - his well-known book and the lesser known but equally important IMO "The Self and Others". He wrote other books too. In it he addresses the very questions you raise in your excellent story. So good, you have inspired me to re-examine a question that is in my memoir "A Long Initiation, Unexpected Magicโ. The question I used to ask in church:
"If there wasn't a Me what would there be?"
Thank-you so much for the inspiration, Alberto.