Generally, open heart surgery is not a painful experience. One notable exception is the removal of the drainage tubes, which typically occurs on post-operative day one. It may feel a bit odd and sometimes can be a brief source of pain. It will feel uncomfortable when you cough, laugh, or sneeze. This discomfort may last for about a month. To alleviate this pain, it is helpful to have a cough buddy (some sort of pillow which is often provided by your hospital). Wrap your arms around the bear and squeeze it against your breastbone when you cough.
During your hospital stay, pain medicine is provided. There is no value in trying to wait until the pain is unbearable before requesting pain medicine. It is far easier to prevent pain then it is to alleviate it. After a few days, most patients just take Tylenol, although narcotics are available on request. A prescription for narcotics is usually provided upon discharge.