Mr. Carr, I have found two men (possibly one and the same man) who may or may not be your Thomas L. Carr. It would help a lot if you knew which side he fought on. Both of these men were in the Cavalry, both were confederate men and both were in Arkansas Regiments. The battle of "Mine Creek", was a Cavalry battle in Kansas. Keep in mind... both men had the name T.L. Carr, and their information match your discription, but I could be wrong on this being the man in question. This is the information I have found with links to see more on this battle and where the [Confederate prisoners were taken after the battle]. This being your primary question, he looks like the same man just different ranks and ;also, did survive the war.
.......
[U.S. Civil War Soldiers, 1861-1865 U.S. Civil War Soldiers, 1861-1865]
Name: T.L. Carr
Side: Confederate
Regiment State/Origin: Arkansas
Regiment Name: Arkansas Cavalry Anderson's Unattached Battalion
Regiment Name Expanded: Anderson's Unattached Battalion, Arkansas Cavalry
COMPANY: B
Rank In: First Lieutenant
Rank In Expanded: First Lieutenant
Rank Out: First Lieutenant
Rank Out Expanded: First Lieutenant
Film Number: M376 roll 4
.......
[U.S. Civil War Soldiers, 1861-1865 U.S. Civil War Soldiers, 1861-1865]
Name: T.L. Carr
Side: Confederate
Regiment State/Origin: Arkansas
Regiment Name: 2nd Arkansas Cavalry
Regiment Name: 2nd Regiment, Arkansas Cavalry
COMPANY: F
Rank In: First Sergeant
Rank In Expanded: First Sergeant
Rank Out Expanded: First Sergeant
Film Number: M376 roll 4

Source Information:

National Park Service. U.S. Civil War Soldiers, 1861-1865 [database on-line]. Provo, UT, USA: The Generations Network, Inc., 2007. Original data: National Park Service, Civil War Soldiers and Sailors System, online <http://www.itd.nps.gov/cwss/>, acquired 2007........

Many irreplaceable Confederate officers were also either killed or

captured. Others escaped by hiding in the brush, while others were shot

or recaptured during their attempts to escape. Lt. Colonel Lazear, 1st

Cavalry Regiment, MSM, indicated a total of 600 prisoners taken,

including 71 teamsters and male refugees. The march back through the

battlefield was a terrible experience for the prisoners, their comrades

laying on the field dead and the cries of agony coming from the wounded.

During the previous weeks of the campaign, many Confederates had

begun to wear captured Union uniforms. Elements of the Union army

had been under orders, while fighting Confederate guerrillas, to shoot

any such captives found to be wearing Union uniforms. Accordingly,

some captured Confederates were shot because they were wearing such

uniforms, while others undoubtedly escaped because of the same.

The prisoners were marched to Fort Scott the following day, a distance

of 26 miles. They were then taken to Warrensburg, Missouri where they

were loaded into railroad cars and taken to St. Louis and prison. Officers

were sent to Johnson’s Island, Ohio. Enlisted men went to Camp

Douglas, and Rock Island, Illinois.

*Source Info:Mine Creek Battlefield State Historic Site>>>>>>>>>>>>>>>>>>>Location
20485 Hwy 52
Pleasanton, KS 66075
Phone: (785) 352-8890

Civil War battlefield and museum.

At Mine Creek in 1864 a large body of Union calvalry swept down on the rear of Confederate General Sterling Price's supply train that was returning south after a long raid through Missouri and Kansas. Today you can walk the battlefield guided by signage to indicate specific areas of interest. Walk the prairie loop and the timber loop trails, both guided by interpretive signage, and visit the newly-constructed visitor center which houses displays on the Battle at Mine Creek, the Price Campaign of 1864, and other aspects of the Civil War.

http://midwestculturaltourism.org/Kansas_files/Mine%20Creek%20Battlefield.pdf About the Battle...

*Information go to :minecreek@kshs.org <minecreek@kshs.org> http://www.minecreek.org/trail_guide/Trailguide%20web.pdf