@kaia I think you did the right thing to take them to the side to discuss it. If they just told you to shut up because you aren't a doctor then this is bad form. I think it would be worth raising with management, because one bad doctor can ruin the experience for everyone else and how things get bad to begin with. If they require authority to listen then so be it.

It is also worth doing for the sake of the patients there, that you are the least impacted so it makes speaking out easier. Just be clear about the outcome that you'd want to see before making the complaint. And you probably know better how to handle conflicts should they arise with teaming up. Let me know how things go.