I have heard and read that the sprouts from potatoes are mildly (or maybe more than mildly) poisonous. I have never known how deep into the potato the toxin could go. But if the potatoes you mention were sprouting (rather than rotting), and if whoever prepared them did not trim away enough of the sprout, then that might cause some sickness.
However, I personally don't believe that it would be a three-week long sickness, but possibly something more like food poisoning. That is just my opinion and not based on any actual medical knowledge about potatoes and sickness.
Your very best bet is to tell and ask the doctor about it, as Sweetsusieg wrote.
The smell of rotting potatoes is indeed one of the worst ones that can happen inside anyone's kitchen.