I currently live in Florida and work for a company out of New York. While in Florida, I pay no state taxes. The problem is that I am now working Georgia and South Carolina. They are taking taxes for each state. I don't see how this is fair seeing as I will never benefit from this. Can I file to get the money back from both of these states? Do I need to pay any at all? Thank you for your help.

If you are present in a state, then you must report all the income you earned while in that state. You must file tax return as part year resident or non-resident (if you just commute to the state).
Depending upon your tax return, you will have a refund or will pay tax due.