I have found this to be my most frustrating research experience, and it continues even now.

For many years, I have tried to reconstruct the activities of the exchanged POW units that were released at Vicksburg. For most of the Fall of 1862, many of these units left very little in the way of recorded history.

Many of these regiments were now under strength due to their prison experience, and thus, many were consolidated to form a suitably sized field regiment. Certainly, that adds to the lost identity and vague awareness of what was happening to these regiments for the last 3 months of 1862.

Regarding the 48th Tn, here are some notes that offer a time line and route of the regiment after release. These notes were compiled from a variety of sources.

I have also listed some sources for more information about this regiment.

Here's hoping your search is more fruitful than mine has been over many years.

Miscellaneous collection of notes in my files:

The officers left their prison on 1 September 1862 and were released at Vicksburg on the 16th. On 3 September, jubilant enlisted soldiers left Camp Douglas and were released on the 23rd. They were in the words of Campbell "relieved of the presence of the hated Yankee once more." Shortly after the exchange sixty-year old Captain George W. Gordon, the well-loved commander of K Company died. The entire regiment mourned his loss. After the enlisted were freed on the twenty-fourth, they were able to spend a few days in Vicksburg. The newly freed soldiers poked around Vicksburg and found it, "A nice place with little to eat."

On the twenty-sixth, the troops boarded "the cars" for a forty-five mile train ride to Jackson, Mississippi. There on 29 September, after seven months of captivity, the 48th Tn was reorganized.

on 7 October, the 48th boarded the cars for Holly Springs

On the twenty-eighth of October the 48th arrived at the mighty Mississippi River Fort at Port Hudson.

Sources for additional information:

Tennessee State Library and Archives
For more detailed instructions on borrowing items through ILL, go to: http://www.state.tn.us/sos/statelib/pubsvs/mailill.htm

Jasper Doggett, Wartime Diarist:
His diary is available through the efforts of the Tennessee State Library and Archives microfilm project
the Jasper Doggett diary has been microfilmed and you can borrow it through interlibrary loan (ILL). Ask your librarian to request Microfilm #824 (Civil War Collection), Reel 2. The Doggett diary should be near the end of the reel in Box 6, folder 7.

Major Andrew Jackson Campbell.
Campbell was born in Maury County on 14 February 1834, into a well-to-do family. He attended Franklin College and mustered in the 48th as a first lieutenant on 17 November 1861. Campbell was captured at Fort Donelson, imprisoned at Camp Chase and Johnson's Island, and exchanged at Vicksburg. He was elected major at the reorganization in September 1862. Campbell's diary presents an eloquent portrayal of his war experiences until his death in May 1863.

Reams Family papers
Jarret Frazier of Voorhies 48 Tn-elected 2nd Lt brevet at Jackson reorg in Sept 62

And, of course:

Tennesseans in the Civil War, part 1

Hope this is of some help to you.