Please help me determine between "you and I/me"... but with an interjection

Solution 1:

That clause is a "parenthetical". An interjection is

a word or expression that occurs as an utterance on its own and expresses a spontaneous feeling or reaction. It is a diverse category, encompassing many different parts of speech, such as exclamations, curses, greetings, response particles, hesitation markers and other words. Wikipedia

A parenthetical doesn't usually change the grammar of the surrounding sentence. It's just being used here to provide additional information about the previous phrase, "people like you and me". The role of that phrase in the sentence is still as the object, so you use "me" rather than "I".

You could potentially rewrite the sentence into two independent clauses, and then make "You and I" the subject of one clause:

You and I face uncertainty, trials, and trouble; the apostle Peter wrote these words to people like us.