Can you have a heart break?

No. It's a figure of speech, a way of expressing one's unhappiness.

A broken heart (or heartbreak) is a common metaphor used to describe the intense emotional pain or suffering one feels after losing a loved one, through death, divorce, break up, moving, being rejected, or other means.

Heartbreak is usually associated with losing a spouse or loved one, though losing a parent, child, pet, or close friend can also "break one's heart". The phrase refers to the physical pain one may feel in the chest as a result of the loss. Although "heartbreak" is usually a metaphor, there is a condition - appropriately known as "broken heart syndrome" - where a traumatizing incident triggers the brain to distribute chemicals that weaken heart tissue.