Hello and thank you for contacting JustAnswer. My name is Michael; I look forward to assisting you today. Since we can't offer legal advice or give advice on your situation specifically, I'll be commenting about the general legal rules regarding issues LIKE yours.
The Georgia Department of Health gives these instructions on how to modify a birth certificate:
How can I make a correction to a birth certificate?
Obtain a certified copy of the birth certificate from the state vital records office. Circle all changes you wish to make, submit a written request to be provided instructions/procedures for the desired changes. An additional fee of $10 will be required to make the change. Request should be mailed to Special Services, Vital Records,***** NE, Atlanta, Georgia 30319. No information will be provided by telephone for instructions/procedures for change. A review of the record must be made to provide proper instructions/procedures for your individual certificate.
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DISCLAIMER: This is not legal advice and I am not your lawyer. My questions are based on my knowledge of the jurisdiction where I am admitted to practice, my experience on this site over several years, and research on the relevant laws and statutes for your jurisdiction, if any. My information is not advice and you should always speak to local counsel before you act.