Even though your truck is "your place of business" it doesn't qualify for that exception to the weapons carry license in Georgia law. So you still need your permit. You have one, and I assume it's a Georgia permit. It should be good in Georgia and in many other states that have reciprocity agreements with Georgia, but when in those other states you have to follow their laws about how to carry, where you can't carry, whether you have to tell a cop that you're carrying, etc.
Watch out for other states where local cities, villages, townships, and counties are allowed to have their own gun laws that may be tighter than the state laws. Tennessee is such a state that allows local regulation of guns. Georgia has preemption.
The biggest risk you face, I think, is the PERCEPTION that guns are not allowed for CDL drivers in commercial trucks. Plenty of people, including ones who wear badges and have arrest powers, think this is the law. And while you can try to put the burden on them to show you the law that says you can't do something, they might put the burden back on you to show them the law that says you CAN carry in a commercial truck. I'm not aware of a definitive source of such a law. You face a higher risk of being stopped, searched without cause, and having your gun confiscated.