Possible anxiety and depression; how do I deal with it?

My very able and alert 91-year-old mother has always had a preoccupation with her health and I am concerned this is damaging for her. If she gets a diagnosis for something minor, she will research it online (she has full mental faculties) and decide it is something else - a rare and dangerous condition - and therefore won't take the medication she has been prescribed. Or she will decide she knows best how to take the medication and alter the dose.

She will doctor shop until she find a doctor to support this view. I am starting to realize this has been a pattern for many years but I am not sure how to deal with it. I try to go to her appointments because she frequently misrepresents what the doctor has said - when called on this, she doesn't argue and will actually agree she is making things up to support her view - which she says is right and the doctors don't know what they are talking about. She was admitted to hospital this week after persuading a doctor to prescribe something that was damaging and the hospital was furious about the situation and with the doctor. They will talk to this doctor but she will just find another one. Talking to her about this doesn't help - it is like her mind is closed off to any other view. Is this generalised anxiety and how do I deal with it? She comes across to doctors as very bright, alert and persuasive - and they seem amused that a 91 year old is researching things on the internet.