I don't know how to counter the argument
Because there isn't a good counter for the base assumption, that public health (as determined by doctors and/or the government) overrides our constitutionally protected rights.
NO one (or no one sane, anyway) questions the authority and moral correctness of a quarantine when a deadly transmittable disease is involved.
The problem is that while they have the authority to determine the what, where, and when to take actions in dire emergencies, there's not a lot beyond common sense that keeps them from deciding what is, and isn't something within their authority for action. And what suitable action is.
Define anything as a disease, and that puts it squarely under their authority.
Everything in our environment, literally everything has a potential impact on our health, and we are the public, so therefore, anything they want to choose becomes the public health "crisis" de jour.
"Public Health" concerns are the ultimate umbrella for authoritarian control "for our own good".
All well and good for society when one is dealing with a deadly plague, but unchecked that power can lead all the way to where disagreeing with those in power, about anything, being classified a mental illness, rather than a valid political opinion.
After all, if you're "sick" you're not in your right mind, and therefore they don't need to respect your opinion (about anything) or, your rights, now do they?