Despite its form, this has nothing to do with poetry (or noses). The first part is from Greek nosos, a disease, while the second is a disguised form of poietikos, creative or productive, which is the source of the English adjective poietic with the same sense plus a number of specialist compounds, including galactopoietic, relating to the production of milk, and morphopoietic, of the formation of organic structures. So something nosopoetic causes disease.
You might think the term would have found favour with doctors, as it would be a useful addition to their vocabulary. It never caught on, however — despite appearing in a couple of glossaries of medical terms in the early nineteenth century — and around the middle of the century was supplanted by pathogenic.
Nosopoetic was invented by the extraordinary mathematician, physician and satirist Dr John Arbuthnot, who also created the persona of John Bull who symbolises the English character and nation. He introduced nosopoetic in his work of 1733, An Essay Concerning the Effects of Air on Human Bodies.
More than a century later, it appeared in a work I’ve had cause to quote from previously, written by a pioneering educationalist in Indiana to encourage students to learn new words by putting them in context:
The multifarious cibarious substances engorged into inane and jejune stomachs, during the nuptial festivity, were extremely nosopoetic on the guests.
Letters to Squire Pedant, by Samuel Hoshour, 1856.
Cibarious means relating to food, or edible; inane is being used here in its ancient sense of void or empty; jejune is likewise in its earliest meaning of fasting or being hungry. This periphrastic conglomeration may be reduced to “The wedding guests became ill from overeating on empty stomachs.”