Shakespeare was probably the first to use this expression, possibly describing the difficulty of being stuck in the pickling liquid made from brines and vinegar, used to preserve food.
ALONSO: And Trinculo is reeling ripe: where should they Find this grand liquor that hath gilded 'em? How camest thou in this pickle? TRINCULO: I have been in such a pickle since I saw you last that, I fear me, will never out of my bones: I shall not fear fly-blowing.