It is hard to tell if you have a rib fracture or just a chest contusion (bruise). Rib fractures can be diagnosed with X-rays or CT scans of the chest. In general, rib fractures are treated with pain control and time, so your father is correct. Because of the abundant network of muscle and connective tissue holding each rib in place most rib fractures are actually held in place pretty well and heal fine without a need for repair.
Rib fractures are mostly encountered in trauma patients (assault, car accident, fall, etc). There was a time when rib fractures were repaired by surgeons
where the ribs were "plated." meaning the two ends of the ribs were aligned and a metal or plastic plate was place over the fracture and screws or sutures were used to secure everything in position. However, we as doctors
and surgeons have gotten away from that because all of our studies that compared outcomes of surgical intervention vs watchful waiting failed to show any advantage with respect to healing time, function, pain, etc. In essence, we found that the surgery just added expense without any actual benefit. Because of this, most simple rib fractures are now treated conservatively, non-operatively. I would still recommend that you get checked out by your primary care doctor
and get at least a chest x-ray to diagnose or rule out rib fracture(s). The other reason to get a chest x-ray is to rule out a pneumothorax ("dropped lung") which actually can be life threatening and would need a temporary chest tube or catheter placement. If you notice shortness of breath or difficulty breathing, you should proceed immediately to the closest emergency room.