Unfortunately, I do not practice law in the state of Georgia. Based upon my experience in the state of CA, the majority of background checks are based upon the Department of Justice database and show felony and misdemeanor convictions only. If you were found "not guilty", you were essentially not convicted of any crime and thus that particular case should not show up on a background check. However, some background checks indicate "arrests" in addition to misdemeanor and felony convictions. Therefore, it is critical to determine what exactly the background check is showing. Meaning, is it showing a conviction for a crime, the filing of a charge for a crime, or is it showing an arrest.
To begin your research, you might want to request a recent background check to determine what exactly is coming up on your criminal history. Then, it would serve you best to contact a criminal attorney in your area to look into the matter, and ultimately see if there is anything that can be done to clear this up. There may be several explanations such as clerical error, identity theft, or may be more specific to the laws within the state of Georgia.
DISCLAIMER: This does not consitute legal advice, but is merely a discussion based upon general legal principles.
Typically, charges stay on your record, even if you are ultimately not convicted of them (though it might be a good idea to contact an attorney who specializes in pardons and expungements to get a second opinion). One thing you can do is contact the Court or the District Attorney's office and request a copy of the Order dismissing the charges against you. Presenting that to your prospective employers may help.