Hi! I'm trying to trace the movements of my ancestor's unit in 1863-1864. I have a series of letters but I'm missing some information.

Here's what I know:

Jacob Grimmett joined up at Camden on March 14, 1863. 33rd Arkansas Infantry, Company C (Radford).

March 20, 1863 - Arrived at Little Rock

April 19, 1863 - At Little Rock

May 9, 1863 - At Little Rock

May 19, 1863 - Still near Little Rock, but moved to a place called Camp Price about 4 miles southwest of town.

March 11, 1864 - Lewisville, Arkansas

March 26, 1864 - Shreveport, Louisiana

May 12, 1864 - In the hospital at Keachi, Louisiana with "Inflammatory Rheumatism"

May 22, 1864 - Died at the hospital, buried in the cemetery nearby

Can you help me figure out where my ancestor may have been from May of 1863 to March of 1864? Did his unit fight at any particular battles?

Thank you for any help or suggestions!