I'm unsure how to proceed here, as I'm not familiar with any empirical work on the social development of the self. The only thing that occurs to me when I think of self in this context is the maxim of the philosopher Descartes: "Cogito ergo sum." I think, therefore I am
. You could take this further and look at the way thought shapes identity - especially as there are such different ways of thinking. (Candy, for example, thinks entirely in 'pictures, concepts, and ideas without words'; whereas I have an extremely weak visual memory and recall my parents' faces with great difficulty.) It would be useful to read some Descartes and bring him into your essay at some pont, as Dennett's theory of self is all about narrative - and what is thought but a species of narrative?
In literary terms, we call the ongoing narrative inside a person's head 'stream of consciousness'. All of Virginia Woolf's novels make use of this technique -she writes in a scattered way, replicating the natural flow of a person's thoughts rather than the coherent narrative structure that we are familiar with. That, too, would be an interesting avenue to explore.
However, I have no idea whether this is what the question is requiring. I don't have the necessary scientific knowledge for it. I can't bring in empirical studies as I don't know any. But I hopes this helps. Let me know how it goes - it sounds like a really interesting essay topic.