You should be able to get a copy of any 911 call because they are considered a public record. Depending on where in the country that you are you should be able to get it from your local police or sheriff's department.
Go to the police department in the town you made the 911 call in (or whatever police, sheriff, or state police Dept that responded to the call). If it was a medical call it might also be the fire dept dispatch. Some towns use a call center that handles multiple towns. When you find that dispatch center, ask to speak the the communications supervisor. He or she will inform you how to request a copy of the call.