To get something off your chest is to say the thing that has been troubling you. Go on, get something off your chest.
The relief is in the saying rather than in any answer, which is why listening is usually enough. The weight on the chest is the picture, and it is an old one.
1phraseget something off your chestTo say the thing that has been troubling you.
“Sit down and get something off your chest before you burst.”
get something off your chest is a phrase.
Practised in Idioms