Would chest pains be caused by a heart issues if someone is 24 and takes good care of their body (e.g. exercise, eating, etc)?

Always possible. any unexplained chest pain ,especially left sided chest pain or pain behind the sternum, must be evaluated immediately.
Chest pains. Though much less likely than in an older individual a cardiopulmonary cause should always be considered; chest pains must be assessed to determine the cause.