Yes it is.
One such idiom is "Don't look a gift horse in the mouth."
Unless there is truly something wrong with your heart, then yes, it is an idiom. My heart fell, my heart exploded, my heart sang, my heart doing anything other than pumping blood is an analogy and an idiom.
An appropriate occasion to give a heart locket necklace as a gift would be any kind of occasion. Wedding Anniversary, Mother's Day, Valentine's Day, and Christmas are a few occasions one could give a heart locket necklace as a gift.
It means to feel that there is no way to go on and you just want to give up.
Idiom
on my way to the hospital
A nice and thoughtful gift from your heart :)
It is not an idiom. Unkindness is often called heartlessness, and so the expression "have a heart" means "Do not be unkind."
I'll give it everything I've got.I'll give it my all.I'll work my heart out.I'll give it my best shot.I'll put my heart into it.I'll put my best foot forward.
"A heart of stone" is a personification.
It is an idiom, because it does not use the term "like" or "as".
A gift from the heart is not the most expensive gift. It shows thoughtfulness. Perhaps a gift of wildflowers rather than a dozen red long stemmed roses would be appropriate.