Is it really dementia?

My sister recently had memory lost, headaches and hallucinations. She was in the hospital for 5 days and after running so many test and really not knowing what was diagnoses they said she has onset Alzheimer. We have a history of Alzheimer disease but l was very doubtful because l had the same symptoms l autoimmune i and encephalopathy and a very high ana. When l went to the Mayo Clinic they did a PET to see if l have dementia and it csame back normal. I read up about autoimmune encephalitis and it told about all of the same symptoms and they said many symptoms are the same but sometimes people have autoimmune encephalitis and not Alzheimer and they want to get the word out because sometimes a patient can be misdiagnosed. They put her on dementia meds. Now she was falling, headaches and hallucinating so l asked the doctor can she habe a PET test, he told me they don't do it at the hospital only the teaching hospital. At first he didn't know what l was talking about. Today we went to the primary care physician and the meds her neurologist gave her she was having an allergic reaction. So the doctor took her off. I told her l wanted0] her to have a PET. She told me she wasn't a doctor and they know what they are doing but it says a PET tells you if you have dementia or Alzheimer. So l really don't want her to get worst when it can be only an autoimmune encephalitis since sometimes it can be normal. I just don't know what to do. Sometimes if its in your family right away you are diagnosed with the same illness because the doctors don't want to just want to run another test. And if l didn't go to the Mayo Clinic l would have had the same diagnoses.l always wanted her to go with me but she said we have doctors here but we are so far behind in medicine in my state. We rate 48 out of 50. And they want to get this out to the medical community so they will look at symptoms being autoimmune encephalitis. She doesn't go back to her neurologist until July because we have a shortage of neurologist. And back to the general practie doctor because he took her off the dementia because an allergic reaction which the neurologist said she should continue because her body was getting use to the medicine. Her head been hurting since she went into the hospital and her high blood pressure is at stroke level most of the times. And the general practice doctor took her off the med she is allergic to and gave her a diuretic for her pressure.