Your spelling of the name in the title line is correct.
Thomson is the county seat of McDuffie County, created after the war from Columbia and surrounding counties. Antebellum Thomson could be found in Columbia County.
The most notable unit from Thomson was the "Thomson Guards", Co. "F", 10th Georgia Regiment.
Here's a roll of this unit --
http://colquitt.k12.ga.us/gspurloc/Cobbslegion/gasca/roster/10th_reg_f.htm
A book about this company has been published. Further information can be found in this page on McDuffie County history --
http://www.rootsweb.com/~gamcduff/resources.htm
Other companies from Columbia County served in the 16th, 37th and 48th Georgia Regiments.