Costocondritis is one of the most common causes of chest pain of non-cardiac origin. The location is not usually the rib/sternum interface, but at the junction of the osseous rib and the costal cartilage which is somewhat lateral and more or less corresponds with the nipple line.
Pain from costochondritis is more sharp than cardiac pain (another word describing it is angina) and it is positional to some degree and is exacerbated with pressure on the local of the rib/costal cartilage interface. A steroid injection in that area is usually remedial, and a little lidocain and marcain, both local anesthetics, helps the uncomfortable feeling for a shorter and longer period, respectively.
This condition exists more commonly at the T-4 through the T-12 rib levels. That means that the sharp pain is more common in the area just below the arm-pit crease on the left and then below that towards the waist line. Surprisingly, it is common in the lower thoracic area at the level of T-ll and T-12 vertebrae, but it is not confused with discomfort from the heart, but with pain from the abdomen. There are plenty of patients who have undergone multi-thousand dollar work-ups for abdominal pain, even exploratory surgery, only to find out they had costo-chondritis of the 11th or 12th rib and referred pain medially into the abdomen.
When I was a new physician I was "bit by that problem" more than once until I figured it out. Often the patients are overweight in the abdomen and the "fat load" pushes out the ribs and causes a physical stress at the costal cartilage/osseous rib location and it is vary painful with increased pain with pressure on that area, moving, twisting, etc.
Pericarditis is another cause of chest pain which is cardiac, but not related to coronary artery disease. The heart beats within a membrane which insulates it from non-moving structures around it. It secretes lubricating material between itself and the epicardium, or the outer layer of the heart which decreases the friction between the two as the heart is contracting and expanding.
Various diseases cause vascular inflammation (rheumatoid arthritis and lupus erythematosis are systemic diseases which includes a vasculitis from an autoimmune source) which becomes worse with compression and abrasion. This heightened inflammation causes pain as the heart beats. At times an examining physician can hear a "friction rub" as the heart beats. It is positional to some degree in that certain postures, such as leaning forward, seem to lessen the pain. Information in "Harrison's Principles of Internal Medicine" indicate that over fifty percent of patients who have rheumatoid arthritis have signs of pericarditis on autopsy. Most of the patients had sub-clinical pericarditis and never felt pain, but the remains of it can be seen on autopsy, as I mentioned.
Another source of chest pain is esophagitis which is nick-named "heart burn"! It is caused by autoimmune vasculitis also, but in this case it causes an abnormality in the autonomic innervation of the esophagus. Normal muscular tension is lessened while it is at rest, so that gastric contents, including hydrochloric acid, pepsin, and digesting food can enter the distal esophagus at the esophageal/gastric junction. This reflux of gastric materials, causes chemical irritation to the esophageal lining which causes pain. Antacids help acutely (Tums, Gaviscon, baking soda, etc.), and acid blocking medications including over the counter drugs like Zantac and Pepcid help for a few days unless they are taken repeatedly.