Glycerol, alcohol, and phenol are used for killing nerve endings (the process is referred to as chemical ablation). Chemical ablation is similar to other ablation techniques (cutting, rf thermocoagulation, etc.). All of these procedures have approximately the same success/failure rates, though the area to be ablated may be more amenable to a particular method.
For chemical ablation, the physician locates the nerve section to be deadened, and injects a small amount of the necessary chemical (usually using a local anesthetic to minimize discomfort). There may be some mild burning or itching immediately after the injection, but the discomfort dissipates quickly.
Pain relief ranges from 0% to 100%, and may last anywhere from hours to months. Every person reacts differently, so there's no telling how well the procedure will work for you. Eventually, nerve endings grow back and the procedure will need to be repeated. Ask your doctor a lot of questions before agreeing to the procedure. You may decide to pursue other options (for example, your gabapentin dosage is actually fairly low, and you may be able to increase the dosage to 3600mg/day or more. Best of luck!