I earned money working in Texas, which does not have a state income tax, however I discovered when I filed my taxes I was being assesed taxes on income I did not earn in Georgia, I don't know the law, but I feel this is unfair.

You want the law changed? Contact the governor, your senator, or representative. If you reside in Georgia and earn income in another state, you must file a return. Also, you may be subject to penalty is you don't make quarterly payments to the Department of Revenue.