should I file a compliant against the doctor?

I would like to know if I can file a compliant against a dishornst doctor who constantly tells lies in order to get double money from both the insurance company and me.
He sent me bill with $65, then after I called up, they told me they are out-of-network, so I need to pay the difference.
I told them I was told they are in-network before I went to the office. Otherwise I would find an in-network doctor. After I argued with them, they finally write off my charge.
But after I talked to my insurance company, they said the doctor is definitely in the network and they already paid him.
So I'm very angry at the doctor who constantly made lies. Although things seem to be resolved. But I would like to write a complaint against the doctor.
Do you think I should write the complaint and where I can send this kind of complaint to?
Thanks for any advices!