Hi I'm currently 15, and I've been charged and I've got a criminal record, can I still go to Georgia for two weeks or will they stop me?
Nobody here is an expert on immigration, and I would not trust any advice that you receive here on this topic. You need to contact the US Embassy in your home country and ask them. Probably you will not qualify for an ESTA so will have to do a full Visa.
Are you planning to travel by yourself? If so, then that would also be very problematic due to your age.