I was terminated because of what someone else did during a unemployment hearing he testified that I had nothing to do with it

It is the general rule in Georgia that an employee cannot bring an action against his employer for wrongful discharge when he is an at-will employee with no definite and certain contract of employment. It is the employer's prerogative to discharge an at-will employee with or without cause and regardless of motive.
A county personnel manual does not constitute an employment contract sufficient to change an employee's at-will status, unless the manual provides that an employee can only be terminated for cause.

To the general rule that at-will employees can be freely discharged there are certain well-defined statutory exceptions. These include garnishment, attendance at judicial proceedings, handicap, and activity protected by the Georgia “whistleblower statute.” Since it does not appear from your facts that you fall into any of these exceptions, a wrongful discharge claim would face a steep uphill battle or so it would seem.