My character has gone from "seriously wounded", to "critically wounded" to "nearly dying". Is it now possible for him to actually die from wounds? Should I start putting my affairs in order? (note my character is a priest in case that matters).
No. Either you die or you don't. Wounds can't kill you.
But that's OOC knowledge for you the player only, so you should still put your affairs in order because your character thinks he nearly died.