I suspect the man you are looking for is John Whitmore of Company K, 57th Virginia Infantry. There were no Whitmans in the 57th and there was no company designated "R".
Whitmore, a resident of Botetourt County, Virginia enlisted on July 19, 1861 and was captured at Five Forks on April 1, 1865. He was released from Point Lookout prison on June 22, 1865. Whitmore was 5'10" tall, had black hair and hazel eyes.
As for "Oliver"--- that's probably Oliver H. Givens, also a member of Company K, or less likely, Oliver H. Shelton, a musician in Company D.
I suggest letting someone with a knowledge of handling historic documents and a talent for reading 19th Century handwriting take a look at this piece of history.