Legal Question in Family Law in Georgia

Maybe. If you and her drew up a living together contract, as you should have, the answer is in that contract.

You can try, but a Judge is just as likely to say that this is the risk each of you took in moving in together. Her obligation under the lease was to the landlord, not you. In addition, even if you had a chance at collecting half of 3 months rent, sometimes it is a much better idea to realize the consequences of decisions and move on in life.