Here's the entry for a "Mill Boy" in Gibson & Gibson's Dictionary of Transports and Combatant Vessels, Steam and Sail, Employed by the Union Army 1861-1868 (Ensign Press, 1995) on p. 225:
MILL BOY; sidewheel steamer, armed; 86 tons.
Chartered Jan 8-31, 1863. Reported as carrying a raiding force during Feb 1863 on the Mississippi to the town of Hopefield to burn that place. Pressed Jan 20-31, 1864. Margin note states vessel was lost in White River Jan 31, 1864; she broke her moorings and drifted, striking a snag. Government paid $11,604.59 for loss.
[HR-337, Western Rivers, pp 160-227; ORA, I, 22, 34]
If this is the correct boat, there is also an entry in Way's Packet Directory (#3926), which adds this interesting information:
SW p wh [Sidewheel packet, wood hull] b. [built] Brownsville, Pa., 1857, 86 tons. Owned and operated by Captain Josiah Cornwall, Chambersburg, Oh. He built her as a floating grist mill, and ran a general store aboard plying between Crown City and Gallipolis [Ohio]. Until 1860, she was horse-powered, the steeds operating a tread-mill attached to side-wheels. He added a boiler and a small slide-valve engine in 1860. At the outbreak of war he sold her to others. She was moored at Jacksonport, Ark., on Jan. 31, 1864, when a high wind parted her lines. She drifted against a snag, sank, and later drifted nine more miles and turned bottom side up. Owned then by Mitchell and Johnson, and was grinding grain for the U.S.
[Note: the tonnage listed, 86 tons, is most likely a measure of cargo capacity rather than her displacement tonnage, though it's not explicitly so stated-- it's simply a common circumstance for civilian boats of the era.]