There are several potential causes of these sharp pains that you are feeling. I do suggest that you start by seeing your primary care doctor
about the issue, who will be able to examine your heart and lungs and make sure there is no serious underlying medical problem.
By far the most common cause of these 'twinges' of pain are inflammation or soreness in the muscles between the ribs or in the joints between the ribs and the breastbone. Even if you feel like the pain is coming from 'inside' it is still highly possible that it is coming from the ribs. The fact that the pain comes in twinges and is worse with a deep breath is consistent with this as well.
However, it is always important to make sure that the twinges of pain are not related to a more serious problem like a lung infection, an inflammation of the lining around the heart or lungs, a blood clot in the lungs, or a heart attack or other major heart problem. If you experience any sudden severe pain, shortness of breath, or other concerning symptoms you should go immediately to the emergency room for evaluation; even in the absence of these serious symptoms, you should still be evaluated at your earliest convenience by your primary care doctor.