1. Telephone record: (a) find it from your phone, with called number, time of the call, and duration. Presumably you can find that you called the doctor's office 24 hrs before. (b) You can also ask for the telephone record from the doctor's office for those two days, proving that you only called once, and that call happened 24 hrs before the appointment.
2. With the occurance of the telephone call established,
2.1 You can testify yourself as witness that during that call, you cancelled the appointment.
2.2. With the telephone record, ask who is the receptionist at doctor's office at that time, and call the receptionist as witness.
Swear the receptionist under oath, with the punishment of perjury, ask her whether she received a call from you. She might claim she cannot remember. You can write down the conversation as you remembered, and give her to "refresh her memory", if she still cannot remember, you are done.
A lot of hassle for $100. Get a life, man.