What is your father is referring to is Pectus Excavatum.
Pectus excavatum is a disorder of the ribs and sternum – or, more precisely, of the cartilage that connects ribs to the lower part of the sternum or breastbone. Someone with mild pectus excavatum will appear to have a slightly sunken area in the middle of the chest; more extreme cases look like the front of the chest is caved in or funneling inwards.
Although the cause isn't clear, there does seem to be a genetic factor in pectus excavatum and it typically shows up in families. About one third of children with signs of pectus excavatum have a close relative with the condition. In 80% of people with funnel chest, the defect is noticeable at birth. In other cases, it becomes visible during puberty, when bones grow and the condition becomes more pronounced. It may be totally superficial, but in some cases it can affect the capacity and function of the heart and lungs.
In some cases, pectus excavatum can be completely harmless and is only a cosmetic problem; in other individuals, it can be very dangerous. This depends almost completely on how severe the indent in the chest proves to be.
I don't believe you had a heart attack. More likely it was an innocent spasm of coronary vessels. With an enlarged heart and pectus excavatum, there can be an additional crowding out effect of the organs within the chest wall that can be problematic.