The gross negligence clause in Georgia is not as solid as it once was. In this case, by fact that you say it's not an emergency, then gross negligence clause wouldn't apply and you could be held liable. It's a catch 22. You discharge the patient, and you could be held liable for ordinary negligence.
The case was tested with Wadsworth vs Houston Medical Center Complex. A patient presented with leg pain, was evaluated by a PA, had documented pulses (albeit weak pulses), had a negative DVT ultrasound, and was discharged with a diagnosis of cellulitis. It was documented there was some erythema. The patient was found unresponsive later in the day and was taken to the Medical Center of Central Georgia. A physician documented weak pulses, but a CTA showed an occlusion. The patient ultimately lost both of her legs.
The defendants own expert witness messed up by acknowledging that you can have a blockage with faint pulses. The jury was tasked with determining whether the defendants were grossly negligent, ordinariliy negligent, or not negligent. The jury determined they breached ordinary negligence. The judge decided that gross negligence protection didn't apply to this patient because OCGA § 51-1-29.5 excludes non-urgent patients in stable conditions.
There has been discussion for bringing this back up for additional laws or possibly putting it before the voters (similar to what Texas did).