It sounds very like a heart attack! But, other disease can also present chest pain like this.
It's consistent or paroxysmal? is it related to physical exercise? will deep breath worsen it? how old are you ? have you ever been diagnosed with digestive ulcer?
A few life-threatening chest pain: ischemic heart disease, pulmonary embolism, pneumothorax，aortic dissection. other disease: pneumonia, Ribitis，shingles, Intercostal neuritis，pleurisy（TB ,maybe no fever）Esophagitis, hiatal hernia, esophageal cancer, lung cancer.
you should go to hospital to find out.