My biopsy was ordered by the ENT. I think this is the usual route. I like your idea of polite demand. One of my great lessons of this illness is becoming my own strong advocate. I have had this illness for over 40 years now and I could literally write a book filled with just my experiences of when I had to steer testing and treatment into a direction that was my best interest. Many doctors are over worked (truely) and I see it as my job to be as informed as I can to work with them in my best interest. Ocassionally, polite demand becomes necessary.

One of my favorite experiences (only in retrospect) was during a time when my primary doc was repeatedly cutting short our visits because he was in a hurry. I did my part every time. I wrote everything down that I needed to go over ahead of time so as not to waste ANY of his time. I had a list of things to go over- important things.
This time my doc gets up and says "Well, I'm sorry but I've got other patients to see" . I had been there maybe ten minutes and my list was only half done. I had done NO chit chat, now waste of time at all.
So when he got up and said this and started for the door I pointed to his chair and said "Sit down, we are not done yet."

It shocked me as much as it did him. I am not an assertive person normally but I wasn't going to be treated like that. I had reached my limit.
To his credit, he went back and sat down and said "ok, what have you got?"
We finished my list fairly quickly and he was able to go see other patients.

It is YOUR health, YOUR life, they work for YOU. They are there to help YOU. Yes, it ALL about YOU. YOU are paying them to help YOU.
Ok, I'm getting wound up again. hahaha I hope things go well for you and you are able to be seen sooner rather than later.
I can say with certainty that if I had done nothing but listened to my doctors all these years, done what I was told and didn't question their ideas- I would not be alive. Several times over , I would be gone.