The brother of my gg-grandfather was there as well, in the 4th Texas, Hood's Brigade.
“Wasn’t it the 13th Mississippi that contested the Feds’ crossing of the river at Fredericksburg”
They did:
Battle of Fredericksburg
The 13th Mississippi was deployed on Carolina Street in the town in support of the 17th Mississippi along the river bank, sending ten sharpshooters to assist the 17th. After Federal forces crossed the river the regiment held Princess Anne Street for two hours. Captain G.L. Donald, who commanded several companied of the regiment, was commended by Colonel Carter. The regiment lost 7 men killed, 59 wounded and 14 captured. Captain J.L. Clark was killed by a solid shot early in the day, Captain T.W. Thurman was badly wounded and captured, and Lieutenant J.M. Stovall was missing and supposed dead.
http://civilwarintheeast.com/confederate-regiments/mississippi/13th-mississippi-infantry-regiment/
My ancestor was one of the 14 captured in the battle and held at the Old Capitol Prison, currently the site of the Supreme Court. At some point he was paroled and returned to his unit in time for Gettysburg.