You are right about the UI. This site is for beta testing. We are adding About page in a week or so that will explain more what we do and what those scores mean. We haven't invested in enterprise designs yet.
Having done no research on your market, and knowing absolutely nothing, my armchair quaterback with a blown knee and beer gut says...
1) ditch the insurance search thing, unless you can get an insurance company to pay you for it early. It is too difficult for you to describe the benefit here, and is it in the insurance companies best interest? It's barely in the best interest of the patient...because they don't know enough about what they are searching for
2) Have you figured out a moat around the doctors and knowing their expertise? Data is not a moat. Your algorithm is not a moat. You may be on to something, I have no idea. Do doctors use linkedin? if not, is there an opportunity to build a network for doctors. Don't forget, LinkedIn is still backed by search. Should you be building a doctor-to-doctor focused LinkedIn that operates on linking specialties?
Also, this isn't only about doctor to patient, there is also doctor to doctor learning opportunities.
The problem with #1 of course is "how did I decide what type of specialist I need"? I started by looking for "sleep", not expecting that you had subdivided into different specialists within sleep. Great. Ok, I now have a list of specialists, but how did I know that I needed a specialist in Central Apnea, as an example. If I am qualified to no the specifics of a disease, I'm probably already speaking to a doctor, so ....
Are other doctors the target market? If so, is this the right UI for them? Or would a "LinkedIn for medical" be a better experience, allowing doctors to "connect", review/recommend each other, etc etc
The current UX doesn't actually give any usable info on the doctor, aside from their contact details, on the searches I've looked at. I have no idea what your "Expert Physician", or "Expertise Team" rankings mean. Or the "Clinical Trials" phases. There are no links for me to do anything.