Do I need to apply for a new 60-day extension at the same immigration office that processed my medical extension?

In THEORY <- meaning how the system is supposed to work, depending on your original entry (30 day visa exempt, tourist, non-imm, etc) you should be able to go to ANY immigration office where you're staying in thailand and apply for the new 60 day cant leave due to covid extension.

BUT

If you used an agency to get you that medical extension and it was from a province/office you don't use they could question you when you go to apply at your office AND they could tell you to go back there.

It's totally up to them on how they want to handle it.

I think it's going to take you showing up at your immigration office and seeing what they say when you ask them..

I think the real question IS; when you got your medical extension did you go to the immigration office on your own with documents from the hospital/doctor and get your extension OR did you hand your passport and a pile of money to an agency that took it to a province you don't live in, used an office you don't use and got the extension..