For your first appearance in traffic court, you do not need your witness present. If you schedule the case for trial, the witness needs to be subpoenaed to come to court to testify on your behalf. You can try to go on the first day and give your side to the solicitor in traffic court. However, they will want you to plead to something most likely. Please consider hiring a criminal defense attorney for your case. It may not be as expensive as you think. You should not have to have a conviction on your record for anything in this circumstance. An attorney can help you keep this from happening.
Although I don't practice in Georgia, I can offer you some friendly words of advice based upon the facts related in your post.
Frankly, I'm shocked that the police officer would issue tickets to both drivers for running red lights without witnessing either of the two violations. It sounds like the police have a very weak case against you and that if you appeared in court on your own behalf dressed cleanly with a clean license, you could negotiate the dropping of the charges yourself. Since the police didn't witness your accident, they would have to bring in the other driver to testify against you in order to convict you, and that's highly unlikely.
Most people go to traffic court without a lawyer and normally resolve their cases if the cases involve a simple moving violation like yours. If the witness is willing to help, you could bring him with you or go to court armed with a notarized, sworn statement from the witness. If the Assistant DA is unwilling to budge on the charges, you can probably ask her or the judge for a short adjournment in order to consult an attorney and/or to coordinate a convenient date and time for your witness to come to court.
I would caution you that since I'm not licensed in Georgia, you should probably talk with a Georgia attorney at some point in time just to verify the procedure in traffic court. I have several colleagues in the Atlanta area and could easily recommend you to a competent attorney if you need one. Please feel free to contact me via e-mail if you have any questions in that regard.