Boromir received a wound in battle that caused him agonies throughout the few remaining years of his short life. This is the first specific reference to a 'Morgul-wound'. The Nazgûl and their weapons were far older than this, and we have to assume that Morgul-wounds long predated Boromir's unfortunate fate.
The name 'Morgul-wound' cannot have gone back farther than III 2002, when the Nazgûl occupied Minas Ithil and caused it to be renamed as Minas Morgul. (Strictly, the word morgul means 'dark sorcery', so a Morgul-wound could be any evilly magical wound, but context, and the fact that the word is always capitalised, implies a connection with the place rather than the concept.)
The Nazgûl themselves dated back to about II 2250, more than three thousand years before the capture of Minas Morgul. It seems unavoidable that they inflicted dark wounds at some point during this long period, but those wounds must have been known as something other than 'Morgul-wounds'.