PRIAPISM
priapism
(noun) condition in which the penis is continually erect; usually painful and seldom with sexual arousal
Source: WordNet® 3.1
Etymology
Noun
priapism (countable and uncountable, plural priapisms)
(pathology) A potentially painful or harmful medical condition in which the erect penis (erection) does not return to its flaccid state (despite the absence of both physical and psychological stimulation), often as a result of a spinal injury.
Obsessive focus on one's genitals or on the need for genital gratification.
Source: Wiktionary
Pri"a*pism, n. Etym: [L. priapismus, Gr. Priapus the god of
procreation, the penis, Gr. priapisme.] (Med.)
Definition: More or less permanent erection and rigidity of the penis, with
or without sexual desire.
Source: Webster’s Unabridged Dictionary 1913 Edition