There is a bibliography containing critical reviews of Capote's works at the eNotes link below. Another source of a critical review (at the link below; see the full citation below) is "Daylight and Darkness, Dream and Delusion: The Works of Truman Capote" by Craig M. Goad.
Goad notes that "My Side of the Matter" is important among Capote's early stories for introducing the kind of protagonist who disturbs an already existing society. As Goad notes, the protagonist in this short story improbably triumphs over the rest of the household, and he establishes a pattern for Capote's future lighthearted protagonists who enforce their own will on the world around them. Goad refers to these kinds of characters in Capote's stories as "utterly independent, often amoral rogues" (36). Goad also feels that this story is not entirely satisfactory and notes that it closely resembles Eudora Welty's "Why I Live at the P.O." He notes that at the end of the story, the protagonist is completely removed from the world around him. Later, Goad compares the protagonist in this story with others of Capote's characters, including Holly Golightly, who can disturb the normal functioning of the society around them (49).
Another critical review is Michael W. Smith's Understanding Unreliable Narrators (see the full citation and link below). Smith uses "My Side of the Matter" as an example of a story with an unreliable narrator. Smith states that the narrator's choice of words immediately places the reader "on the alert" that the narrator's version of events is unreliable (16). The narrator also makes his own self-promotion and self-concern so obvious, according to Smith, that this is a story in which the narrator's unreliability is clear to the reader from the beginning. He contrasts Capote's stories with other stories in which the unreliability of the narrator is not as obvious. There are other sources about Truman Capote's work at the eNotes link below.
Goad, Craig M. "Daylight and Darkness, Dream and Delusion: The Works of Truman Capote" in The Emporia State Research Studies, Volume XVI, September 1967.
Smith, Michael W. Understanding Unreliable Narrators: Reading Between the Lines in the Literature Classroom. National Council of Teachers of English: Urbana, Illinois, 1991.