Why antibiotics? If the culture was obtained from a surface swab, it is not valid since 1994! also, what is the reason for the open wound of the leg? Before your doctor treats anything, he/she should provide you the reason for the slow healing. Infections rarely "smolder". They make things worse fast so if this is not the case, then infection is quite unlikely. Everything has bacteria as a contaminant.
Antibiotics. The fact that you know that it is a gram negative bacteria means that your clinicians also know what the sensitivities are. They are in the best position to evaluate this. There are hundreds of gram negative bacteria with endless combinations of sensitivities so that no one is able to give that answer to you on line.