Company health check follow up. How much do I have to divulge?

Had a minor health issue get flagged during my healthcheck last year.

I have followed up with doctor about this on my own and am dealing with it. However the health department at my company has been emailing me asking about it.

They want to to know things like what clinic Im following up with, what the doctor said, results of follow up tests if any, etc. I feel like this is way too invasive of my privacy.

I already wrote back saying Im talking to a doctor and will deal with taking care of the issue based on doctors advice on my own.

They havent responded yet, but if they push the issue Im curious if there is any actual law or rule or something that I have to divulge this info since they provide my insurance.

Can I keep telling them to kindly fuck off or do I actually need to provide them with this extra info?