Student or Learner
Archer fished in his pockets again, and this time he produced a paper napkin. I took it from him and gave Lady Macbeth a run for her money in the hand-scrubbing department. But even as I attempted to remove a layer of skin from my finger, something was bugging me. I mean, something other than the fact that I’d just touched a puddle of blood.
gave Lady Macbeth a run for her money in the hand-scrubbing department ??
(Wikipedia)Lady Macbeth is a fictional character in Shakespeare's Macbeth (c.1603–1607). She is the wife to the play's protagonist, Macbeth, a Scottish nobleman. After goading him into committing regicide, she becomes Queen of Scotland, but later suffers pangs of guilt for her part in the crime. She dies off-stage in the last act, an apparent suicide.
She became a compulsive hand-washer to get rid of the blood on them.
In your quote the writer exaggerates somewhat by saying that he/she exceeded even Lady Macbeth in this compulsion.