Dull, but slowly building pain in chest around sternum. eventually left. what is it?

Many possibilities: In many cases, this is related to muscles or ligaments in the chest however depending on your age, other symptoms and risk factors for heart disease and other ailments you might need an evaluation for a heart, lung or stomach problem. See your doctor soon about these symptoms and if they are persistent or progressive, along with symptoms like shortness of breath or dizziness, go to ER.