You will need to check the language of your sales contract. Most of the time, it will be written that the pro-rated property taxes will be part of closing costs. In general, If you've already paid taxes, then the buyer will pay you the pro-rated portion of that, from the closing date through the end of the year. If you haven't, then you would usually be charged the pro-rated amount to be held in the buyer's mortgage company escrow account, with the remainder being collected from the buyer at a later date.
For your income tax purposes, you can deduct that tiny amount of the paid property taxes from your income (assuming itemized deductions).
Doing some research on property tax for the state of Georgia brings up this interesting note:
If you owned property on January 1, you are responsible for the ad valorem tax for the entire year even if you sell the property on January 2. Georgia law does not allow a refund for partial year residents.
This leads me to believe that your sales contract would have it written in that the buyer paid you almost the entire year's property taxes in anticipation that you would be responsible for the property taxes, as you owned the property on January 1st.
Again, you should consult with the settlement attorney and review your contract.