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As far as I can see, Forrest never spoke or wrote about the incident with the Union soldier publicly while he was alive. However, the story of how he was seriously wounded at Shiloh appeared in several books printed soon after the war, including at least one where Forrest seems to have collaborated closely with the authors.
The story about Forrest using a Union soldier as a human shield seems to have first appeared in the 1902 biography written by Captain James Harvey Mathes with the slightly unimaginative title, 'General Forrest'. Mathes, in turn, claimed to have heard the story from Forrest's son, Willie, who had also been present at the battle.
The story about using a Union soldier as a human shield certainly doesn't appear in The Campaigns of Lieut.-Gen. N. B. Forrest, by General Thomas Jordan and J.P. Pryor. This was written in close collaboration with Nathan Forrest himself, and was published shortly after the war, in 1868. (The account of the incident appears on pp147-148).
This account does, however, record the injury that Forrest received at Shiloh, which - it was thought at the time - might have proved fatal. Clearly, in the event, it obviously wasn't.
The story is certainly repeated in many biographies and accounts of the battle published after Mathes work was published. To be honest, the story is probably just too good for any historian writing for the public to ignore!
We can also be sure that Sherman was present during the incident. We have this from a dispatch included in Sherman's memoirs:
The enemy's cavalry could be seen in this camp; after reconnoisance, I ordered the two advance companies of the Ohio Seventy-seventh, Colonel Hildebrand, to deploy forward as skirmishers, and the regiment itself forward into line, with an interval of one hundred yards. In this order we advanced cautiously until the skirmishers were engaged. Taking it for granted this disposition would clear the camp, I held Colonel Dickey's Fourth Illinois Cavalry ready for the charge. The enemy's cavalry came down boldly at a charge, led by General Forrest in person, breaking through our line of skirmishers; when the regiment of infantry, without cause, broke, threw away their muskets, and fled.
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This site (the American Battlefield Trust) has a quote from Sherman talking about the incident.
https://www.battlefields.org/learn/maps/battle-fallen-timbers-april-8-1862