Does the "my" refer to Deku as in the school he goes to or is it a collective reference to the audience/readers/viewers or both?
As it was pointed out, the very first chapter contained a narration part where it's made explicit that this is a story hero Deku is recounting about how he became the greatest hero (which may be why there's such a stark contrast between the Deku that's shown to us and the perception the rest of the cast has of him).