The Civil War Soldiers & Sailors System is online at
A couple of issues to consider in your search:
Variations in spelling are common. You should search for every conceivable variation of the spelling of Nichols.
The first and middle names are quite common. You should also consider every variation such as George, George W., G.W., Wash, etc.
You should be open to possiblity that his rank was other than "captain". You should also be open to the possibility that he was in the Union Army, instead of Confederate, or possibly switched to the Union side during the war.
If he was in Grundy Co. on the 1860 Census, it is likely he was in a unit raised in Grundy Co. -- and perhaps originally in the Missouri State Guard. Others on the message board can probably help with what units were raised in Grundy Co.