A scratchy throat was an irritation at the back of one’s throat.
In 2153, Jonathan Archer complained only of a scratchy throat as a supposed symptom of xenopolycythemia when examined in prison by Phlox on Narendra III. (ENT: "Judgment")
In 2378, The Doctor, posing as Chakotay, claimed to have a scratchy throat while speaking huskily to Tuvok. (VOY: "Renaissance Man")