This is something that people say when they feel like they might be having a heart attack.
Saying that you're "having chest pains" sounds more serious than "My chest hurts."
"Pain" is usually uncountable, but sometimes people also talk about "pains". The most common examples are:
- chest pains
- labor pains (when a woman is having a baby)
- joint pains
- stomach pains
These examples describe sharp pain which comes and goes for a few minutes at a time.