According to Serving with Honor: The diary of Eathan Allan Pinnell of the eighth Missouri Infantry (Confederate) by Michael Banasik, there are two entries:

Frazier, W.H.L., Field and Staff, Enlisted October 5 1862 at Elm Springs, Arkansas, Major, Oranizized a Battalion of 3 infantry Companies at Elm Springs, AR; Combined with Mitchell's Batalion of 6 infantry companies November 29, 1862. Resigned because of a leg injury Feb 18, 1863.

Frazier, William H., Company G and K, Impressed for 3 years service (Fraziers Battalion, company A), Sept 1-20, 1862, 3 Yr CSA service 20 Sept 1862in Washington Co, AR, Age 22, as a private, Sergeant Major (October 5- December 23 1862) 2nd Lt (Dec 23 - 1862 - ?) Captain (Unknown) Born in Ky, Wounded in thigh at Pleasant Hill, LA April 9, 1864, Cited on Confederate "Roll of Honor"

I( would suggest that you fet thier combined Service records where this information is culled from. My ancestor was in Wingo's infantry, and was at Wilson's Creek, Lexington, MO and Dry Woods Creek. I only know this because i get his application for Pension, and he wrote of his MSG Service, and not CSA service.