The psychic listens to her. The doctor does not. The psychic makes her feel heard. The doctor does not.
People fail to understand that the principle allure of alternative medicine is they get actual face time with a single person who takes notes and writes down what they feel and goes back to study it. You will have an objectively better visit with a tarot card reader than a clinic doctor on facetime alone.
Try it: go to the Minute Clinic for an infection. You will wait two hours, a doctor will see you for two minutes, will give you a prescription for antibiotics that will be filled half an hour later and two weeks later you'll get a bill from your insurance company that says "this is not a bill." Then another week later you'll get a bill from the Minute Clinic that is a bill. Then you'll call your insurance company to fight about the fact that they're only paying $60 of a $180 visit for $2 worth of sulfa drugs. Meanwhile your infection is gone but you've been made to feel like the problem by two receptionists, a nurse, a doctor, a pharmacist and two faceless bureaucracies.
Now go to the tarot reader. The lobby is nice. You pay cash up front. And for half an hour you have the undivided attention of a professional. If the infection goes away on its own, YOU WIN. Besides, you've gotten all this wonderful cold reading stuff to think over. You're learning more about yourself. You are invested in your own health care. You are the captain of your ship and you have a trusty guide to pilot you over unquiet waters.
Your best move is to encourage your sister to find someone with actual medical knowledge that will make her feel heard. It's worth the money. People will do whatever an expert tells them to do if they trust that expert's expertise. She's related to you - she can't be stupid. She's just emphasized her own autonomy over the medical knowledge of busy professionals.