I don't know about good popular histories on it, but The White Death by Thomas Dormany is pretty good for TB - it's not a popular history as such, but it's also not dry academic stuff, either, and includes a lot of the relationship between TB & literature (& culture) & literary people who died of TB (and their descriptions of it) & I found it v useful. (It certainly seemed reliable enough - nothing raised any immediately flags, although obv am not medical nor a professional historian either).

I enjoyed The Arsenic Century (largely about how Victorians kept poisoning themselves) & right now my mind is blanking on any other popular histories, although I know the kind of thing you mean & they're very cool when done right. And not getting basic facts wrong. (If someone's not spotted something that is that simple to double check at any point during writing, editing and proofing, that's pretty bad.)