Given that we are talking about the Third Age, would it be likely that Hobbits would recognize a respiratory illness as in fact "cancer"? Wouldn't they be more likely to have a very different vocabulary for diseases and discomforts?
Cancer became the word for the medical pathology circa 1600--interestingly, because wasn't tobacco introduced to Europe around that time, after the new world invasions? Before that, the word tended to denote the astrological sign and the word "canker" was used for bodily complaints.
I'm sure there's a great deal in medieval medical vocabulary that would be great fun to apply to Middle-earth, in particular relating to spitting, spewing, coughing, hacking, pustules, open sores, running sores, fevers and agues, to say nothing of the theory of humours.
Hmmmm. Hmmm. Do I hear the sounds of an RPG strumming in the back ground here? Yes, a story of why the elves tended not to pay much attention to the hobbits. Perhaps the elves could not stand the experience of watching bodily decline and disability? I wonder if they would be grossed out by the effects of the gift? Certainly death was a great shock to Arwen.
Either that or REB IV, the Last Homely Old Folks Home.