Chest pain due to ischemia (occluded vessels) happens with exertion and goes away with rest and that can be related to the heart cells not receiving sufficient oxygenated blood.
However, when there is chest pain when taking a deep breath can be due to costochondritis....pulled muscle in the chest wall, inflammation of cartilage of chest wall, good be irritation of lung lining, etc. other pulomonary issues.
You may want to get physical evaluation, as a heart problem can't be ruled out, and/or pulmonary malady. The wave you felt may be heart related, and a variation of heart palpitation (irregular heart rhythm) and usually not medically significant such as a skipped heartbeat.