If your wife took goldenseal root for this cold, it could be gone in a day or two.
The coughing, hacking crap you're describing sounds to be bacterial. I think it's the most prevent pathogen which can drag on and on like that. (Although fungus is up and coming so if goldenseal doesn't work magic, try olive leaf)
A couple 3 capsules every 4 or so hours with a hot beverage or cayenne pepper capsule (if she's not the type that overheats easily) and she should be hunky dorey within even 24 hours. I've experienced it, and have given it to friends and relatives with this crap, and it worked equally fast, if not faster (the younger, the faster usually).
Doing a couple doses after the symptoms are gone is a good idea too, make sure you got it whacked completely. You can use the silver in conjunction, too. I never did, but I bet it would make it go even quicker. You could let me know.
The problem so many have with herbs is their bodies just can't metabolize them, so they think, having tried some along the way and saw no improvement, that they don't work, when it's their body's inability to use the herbs.
That's why in the old days, they made a tea of things, and you got some of the worse tasting concoctions ever. Thank goodness for capsules, but at the same time it's unfortunate we have capsules.
But of course as with any antibiotic, replenish her good bacteria after she's not taking it any more. Olive leaf won't need that though.
The most effective healing agents have been stolen from our realm of knowledge. :( And replaced with 'drugs'.