Check the Virginia Slave Births Index. Its a 5 volume series of books that lists the births of (many)slaves from 1853 to 1865. It should be in your library's reference section. You may be able to use that to confirm which Braswell man (or at least which Braswell plantation) you need to focus on. From there go to the library of virgina's genealogy website (
http://www.lva.virginia.gov/). If the will of the owner/owner's family is there, you can search it. Good luck.