Have your company stop the Illinois state income taxes from being withheld from your wages.
You will have to file two state tax returns. The Illinois nonresident state return showing 0 income and the Georgia resident state tax return including all income. You will get all the IL state income taxes withheld refunded to you. You complete the nonresident state tax return before completing the resident state tax return.
When entering your personal information in the My Info section, you enter your resident state as Georgia. You will be asked if you earned money in any other states, answer Yes and select Illinois as the other state.