If you're interested in the idea of the self:community balance in defining the self/individual, (at least from my perspective as a medievalist), the work you want is:

• Caroline Walker Bynum, "Did the Twelfth Century Discover the Individual?", in Jesus as Mother: Studies in the Spirituality of the High Middle Ages (1982), 82-110

And I don't like recommending this because Brill (the publisher) can go DIAF with its prices, but I think might help put you in the mindset of identifying self as/within the family:

• Giovanni Ciappelli, Memory, Family, and Self: Tuscan Family Books and Other European Egodocuments (2014)

The title could not be more dry if it tried ("egodocuments"? one word, really?), but looking at the use of various genres of family-book as collective memory, in conjunction with thoughts on the relationship between memory and forming one's identity, seems like it would also help you fill in some of the blanks.

There's also Charles Taylor, Sources of the Self, but like a lot of 500+ philosophy/theory books, I personally find it more helpful to read reviews and commentaries rather than the original.

...Basically here is a MASSIVE historiography on this. Even a search for something like "medieval self" or "medieval self bibliography" should turn up plenty of fruits. Just don't listen to anything that says the self was invented in the early modern era or after. (Renaissance Self-Fashioning, I'm looking at you.) ;)

Secondly, assuming it is at least partially accurate, how best can I understand this? The very concept of me as an individual being defined by "we" instead of "me" is hard to understand (...) Bonus: Are there any recommended books on the subject?

Questions of historical evolution aside, there's a voluminous literature on precisely this in the psychological literature. This is the paper; also read this.