When I'm in love, I like to skip out of joy.
Your heart "skips" when you're in love
When I'm in trouble, things can get real shocking.
If you have a heart problem, you may need a "shock" from a defibrillator.
You will be sad when I'm broken
Figuratively, a "broken heart" means you are saddened.
but don't worry I can take quite the beating.
Your physical heart "beats"
People will tell you to listen to me
"Listen to your heart" is an idiom meaning listen to your inner voice.
but only smart people will know what to listen for.
Well-educated Doctors know how to listen to a physical heart.
And your title: "I am not the shape I am"
The real human heart is not really the shape of the common symbol used to represent it.