It's like this -

When I say 'you', I mean myself. When I say 'me' - I still mean myself. And when I say 'myself', I'm not quite sure what I'm talking about.

Pronouns for 'persons' have two facets. One that indeed pertains 'a person' - an identity - and then a second one... that doesn't. And, in fact, it's the latter that is more foundational for language. We (which is to say, most of us) dwell in a world of personal identities, but that is not for the pronouns' sake, at all - though it often appears so. What we've done, is we've impregnated one primeval form with another - as if by way of superimposition. 'Identity' might be primeval - but it's still a separate form from the pronominal function. Keep this in mind! - For you might one day find yourself missing the former. (Personal identities do dissolve, deconstruct - medical science calls it 'depersonalisation', and it's not altogether that rare.) And of the plethora of things you will have to deal with then, one is the queerness of the first person pronominals. Viz. there is no person in the 'first person'. Still, despite their awkwardness, you're probably inclined to use these expressions, and use them often. (It's possible but laborious to consistently bypass "I" in speech, for instance.) Thus, I remind you - use these expressions freely and with no quilty conciousness. They bear a function that is independent of the construction of a personal identity, - though it might be that only by time will the sense of puzzlement pass. Such is the depth of our doubly imprinted way of thinking and speaking in 'personal pronouns'.