Legal Question in Real Estate Law in Georgia

That depends in large part on the language of your association agreement, which you have not provided to us.

You will also likely have a difficult time showing that the termite damage was caused by the neighbors, as opposed to termite damage that comes from termites coming from the ground to your walls (presumably, no one planted them in the neighbor's unit). The best thing you can do is take whatever steps are necessary to protect your unit, including getting an exterminator and contacting the manger of the next-door unit.