I have not been able to locate Laomi in my father's books but the problem is not knowing her last name. I have found two Andrew Jackson Calhouns but their mothers are not Laomi. If Andrew Jackson Calhoun is Laomi's son, then Calhoun is her married name. You need to find out what her maiden name was. Quite often, at least one of the children carries her maiden name as a first or second name. Do you have any information on Andrews brothers or sisters?
Birthdates are also the first step in locating an ancestor since there are so many with the same christian names.