This word had its fifteen minutes of fame at the IgNobel awards at Harvard University in October 2001. These annual ceremonies recognise research that, in the words of the organisers, “cannot or should not be reproduced”. The award for Public Heath went to an article, A Preliminary Survey of Rhinotillexomania in an Adolescent Sample, which was published in the Journal of Clinical Psychiatry in April that year. The judges described this as a “probing medical discovery that nose-picking is a common activity among adolescents”.
Rhinotillexomania does indeed mean picking one’s nose, though habitually rather than occasionally. It looks like an example of word invention for its own sake, but it has appeared a few times in scientific publications. I haven’t been able to trace it back very far; an early example commonly referred to is a postal survey carried out by two Wisconsin researchers in 1994; this was written up in 1995, also in the Journal of Clinical Psychiatry, which seems to have a near corner on the term.
The word seems to have been invented in imitation of trichotillomania, an older term for a compulsive desire to pull out one’s hair. This comes, in part, from Greek tillesthai, to pull out. The new word should have been rhinotillomania (from the classical Greek rhis, rhin–, meaning nose), but its authors, unversed in classical Greek, added an unnecessary –exo– (from Greek exo, outside).