Did you work in Georgia or did you work in Louisiana? Money that you earn for working is taxable by the state where you do the work, even if you are not a resident of that state.
If you worked in Louisiana you have to file a Louisiana nonresident tax return and pay Louisiana tax on the money that you earned there. You also have to report the income on your Georgia resident tax return, but you will get a credit on your Georgia tax return for part or all of the tax that you pay to Louisiana.
If you worked in Georgia, it makes no difference where the company that paid you is located. Since you live in Georgia, the income that you earned for working in Georgia is only subject to Georgia tax. You do not have to pay any Louisiana tax on money that you earned for working in Georgia.