I often have an earworm. Like lots of folks.
Today I have what I’m calling a twofer.
From Grease, Rizzos song: “Look at me I’m Sandra Dee, lousy with virginity” that morphs into “I ain’t missin’ you, I’m not missin’ you at all”
(Don’t know what song that is)
Over and over and over.
Think I’m gonna pop some Valium before I start stabbing my head with an ice pick. 
Last night, i was watching an episode of “The Big Bang Theory,” in which Sheldon had an earworm – just a snippet of melody, which was driving him crazy trying to figure out. He finally realized that it was from an old Beach Boys song, and that it was his subconscious telling him that he really did love and need Amy Farrah Fowler.
In your case, the second half of your earworm might be from John Waite’s song “Missing You.”
I won’t be looking it up. But thanks.
I tried the the thing of listening to another catchy song a couple times.
Didn’t work.
Aaaaccckkk!
The one song which is guaranteed, for me, to banish any other earworms is (spoilered just to protect anyone who doesn’t want an earworm):
ABBA’s “Dancing Queen”: https://www.youtube.com/watch?v=xFrGuyw1V8s
Oh god!
Hey, I did put it in a spoiler box. 
I cannot not open those blur spoilers
Love that piano! 
Ding ding, 
deng deng, dong dong! 
Oh. You mean a ‘musical earworm’. I guess I confused it with earwig. I was going to suggest it was actually lice from your dirty possum.
The worst earworm of all time for me…can’t do the spoiler box thing, sorry, is The Chicken Dance. Even now, I’m humming something else to keep it from…dang it, the “something else” is “Dancing Queen.”
Once I mentioned to a student that a song was going through my head, and I couldn’t get it to stop. He asked what song. “Lucky” by Daft Punk. He looked shocked. “Ms. _____, that’s a dirty song!” “I know! That’s why I don’t want it in my head!” I was afraid I’d absent-mindedly start singing it during class.
Anyway, I looked up how to cure earworms. One way was to chew gum. Another was to play the entire song, as earworms are usually only snippets. And there are supposed to be “cure songs” that help, but the only one I remember is “Karma Chameleon,” which I loathe. After school, I chewed gum and listened to a bunch of other catchy tunes, and that worked.
I can bleach out any earworm with Frank Mills’ “Music Box Dancer”.
I tried the Beatles. Seems like ‘Yellow Submarine’ may do it.
I’m afeared I may have gathered a new worm. Gah!!
“Girl from Ipanema” is supposed to be a cure song. I’ve had limited success.
That’s good to know. Beats “Karma Chameleon” any day.
Singing it out worked for Eric Cartman.
I’ve found that playing something raucous helps. No idea why, but my favorite recently is from a duo called Black Pistol Fire. They’re amazingly loud, but this song has great rhythym.
Try “Maxwell’s Silver Hammer” or “Lady Madonna.”
I’ve had earworms that conflated two songs together before, though I can’t think of a specific example right now.
My wife, when we started dating, told me a song cure she came up with for earworms-- focus on the old Suzanne Vega song “My Name is Luka”. According to her, it’s just catchy enough to banish the earworm, but not catchy enough to take over as an earworm of its own. It does seem to work.
How dare you?
Clarence is not dirty.
He’s just mussed up a bit. Who doesn’t wake up with bedhead.
I have you know he owns a cat,
Miss Haricot who spends hours grooming him.
He’s been very tidy since she showed up.
I use Danse Macabre.