I kept thinking about the Beach Boys' "Don't Hurt My Little Sister" because the melody of Brian's falsetto part sounded familiar too. Last night, I finally figured out where I know it from. There's a song by Jay and the Americans called "Things Are Changing," which - in my opinion - is one of the worst in their catalogue. Some of the melodies of the background parts are grating, and the song as a whole seems more like propaganda.
But in any case, it has the same melody as part of "Don't Hurt My Little Sister." I looked it up and was surprised to discover that it was actually co-written by Brian Wilson (with Phil Spector). While looking up the recording dates, I discovered that "Things Are Changing" is pretty much just Phil Spector's revision of "Don't Hurt My Little Sister." From Keith Badman's The Beach Boys: "Brian originally wrote this song for The Ronettes and submitted it to their producer Phil Spector, who then altered the lyrics and called it "Things Are Changing (For the Better)". Brian will recall that Spector kicks him off the session because he 'couldn't play the song right'. Spector later cuts the revamped song with The Blossoms as a public-service announcement for equal opportunities."
The melody of the first part Brian's falsetto section ("why don't you kiss her") remains unchanged in Spector's rewrite ("it doesn't matter"), which is what first caught my ear. But listening to the beginnings of the two songs back-to-back, the resemblance does come across.
The recording dates: The Beach Boys' "Don't Hurt My Little Sister" was recorded on 22 June 1964 and 18 January 1965 and was released on Today! on 8 March 1965. Jay and the Americans' "Things Are Changing" was recorded in August 1965 and released in January 1966.