priapism
noun
pri·a·pism ˈprī-ə-ˌpi-zəm 
: an abnormal often painful persistent erection of the penis
Example Sentences
Recent Examples on the Web Portis’s diffident, modestly gallant characters were a world away from the marital bonfires and priapisms of other male writers of his crop—Roth, Updike, Yates. 
Wells Tower, The New Yorker, 20 Feb. 2020 Lastly, and saddest of all, the Corvette will lose its hood of goodly length, the conspicuous priapism that has defined the mission for 65 years. Dan Neil, WSJ, 28 Nov. 2018
Wells Tower, The New Yorker, 20 Feb. 2020 Lastly, and saddest of all, the Corvette will lose its hood of goodly length, the conspicuous priapism that has defined the mission for 65 years. Dan Neil, WSJ, 28 Nov. 2018 Word History
Etymology
French priapisme, from Middle French, ultimately from Greek Priapos (traditionally portrayed in Greco-Roman art with an erect penis)
First Known Use
1601, in the meaning defined above
Medical Definition
priapism
noun
pri·a·pism ˈprī-ə-ˌpiz-əm
: an abnormal, more or less persistent, and often painful erection of the penis
especially : one caused by disease rather than sexual desire