I had to do the same thing for my novel only instead of a doctor, I needed a vet. It was only one scene but it was very detailed so I needed to get the information bang on.
I think the key to consulting experts is to respect their time.
To that end, I started with Google and did as much research myself as I could so that when I approached professionals I wasn’t asking clueless questions that wasted their time.
Next, I went into veterinary chat rooms (and there are Health and Biology Stack Exchanges you can post to) and formulated educated questions based on my own research. This raised information I hadn’t thought of during my research, and also, inevitably, highlighted problems with my scene which raised further questions.
Next, I signed up for a paid online consultancy with a qualified vet and posed my (now well-informed) questions to her. She was incredibly helpful because she was being paid to do that.
However, none of these routes really gave me a ‘feel’ for the scene I was writing. That took meeting professionals in person at their place of business. I called around three local vets and asked if I could come when it wasn’t busy. One vet was amazingly helpful and booked out a consultancy period free of charge at the practice.
Before meeting her, I put together my list of well-informed questions, took notes during the meeting and kept it as brief as I could.
With respect to health, I would try a private consultant in the field. If you’re UK-based you’ll find that NHS doctors are pushed to their limits and less likely to give you their time. You can use a Bupa search to find a specialist in your area and then contact them via email to see if they’d be happy to do an interview (UK based, but there must be a similar US site):
As I say, the key is to respect their time. Do as much of your own research as you can so that if you can organise a face to face interview, your questions are well-informed and to the point.