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There is a book written about the family The Garlington Family by Scogland 1976
You can find places that it may be available at the following website
You also might want to contact the Virginia Historical Society
Dear Ms. Garlington-Arnold,
Thank you for posting your request on History Hub!
In addition to the information from the previous poster, we suggest that you contact the Virginia Colonial Records Project at the LIbrary of Virginia to inquire about personal property tax lists, business ledgers, or other papers of Green Garlington. Also, please review the FamilySearch research wikis for Halifax County, Virginia Genealogy and Virginia Colonial Records.
For information regarding the Garlington family of Yorkshire, England, we suggest you contact The National Archives of the United Kingdom,and review the FamilySearch Research wiki for England Genealogy.
We hope this is helpful. Best of luck with your family research!