Howdy Janet !
I`ve never been in TX, but what I know of the organization of TST-companys - is that they often changed names and company letters.
The Norwegians in the Frontier regiment was from Bosque, and all was in Co E of the unit. But, as your man, they did change letters of their company - (1st) Co B / (2nd) Co E. They mustered into state service 8 Mar 62 - redesignated Co E 20 Dec 62. The company had men from Erath, Eastland and Bosque counties.
From what I know - you`re likely to find information in the counties the company had men from. You may also contact the local museums in the counties above (were the men from Co E was from) - they may have info about the company you`re searching.
I think this man is the one you should ask - he has written a Master-thesis of McCords Frontier Regiment - http://history-sites.com/mb/cw/txcwmb/index.cgi?noframes;read=3283
Here are some links that might interest you:
I do know that Kathey Hunt at Kaufman Co., TXGenWeb Project site does knows allot about TST-units. http://www.rootsweb.com/~txkaufma/civilwar/civilwar.htm