Chronic cough, indeed, can cause chest and breast bone pains.
I think you may have an acid reflux issue.
When stomach acid is backing up in your esophagus, you may feel burning sensation or pain behind your breast bone.
This may also lead to chronic cough due to chronic acid irritation and reflexes that result in spasm of the airways that can cause shortness of breath and coughing.
Chronic sore throat is another symptom of acid reflux, since chronic irritation of throat due to acid reflux leads to painful or sore throat.

See a gastroenterologist!