ARDS is a syndrome associated with trauma, sepsis, multiple organ failure, etc. It is also known as non-cardiogenic pulmonary edema. Protein rich fluid collects in the lung alveoli, making oxygenation poor. Patients require high levels of oxygen and PEEP to keep adequate oxygen levels.
In my experience, ARDS is difficult to survive. But if you were the young, healthy victim of a trauma (that caused your fracture?), then I suppose that would explain it.
If it was ARDS, I don't think that had anything (directly) to do with the anesthetic, and hence your risk of getting it again is no higher than any other person. Perhaps someone with more recent ICU experience might be able to be more specific.
However, you also mention aspiration pneumonia. If that was the cause of your respiratory failure, then I would be a bit more concerned. You probably had a general anesthetic for ORIF (open reduction internal fixation, in English-setting a broken bone). During induction of anesthesia it is possible for stomach contents to enter the airway structures. If this aspiration is bad enough it can do widespread damage to the lungs, and cause significant problems with oxygenation.
If aspiration was the cause of your respiratory failure, then it would be helpful to examine your anesthesia record. Maybe you were at risk for aspiration because the surgery was emergency, and you weren't NPO.
Most importantly, did the anesthesia provider have trouble getting the endotracheal tube in place? If this is the case, then you are a "difficult intubation" . This is important information for you to relay to your anesthesia provider anytime you have anesthesia. It is only a problem if it is unanticipated. With advance warning, it can be managed fine.
Hope this helps. Good luck with starting your family.