Gabapentin is not a narcotic and is not a substitute for opiates like Oxycodone. Opiates are still the best pain control medications available.
Gabapentin (Neurontin) and pregabalin (Lyrica) are similar medications that modulate pain transmission in the nervous system, but gabapentin and pregabalin utilize a different chemical pathway than opiates. They are both used to treat nerve pain (neuropathic pain), but gabapentin can be useful in treating other pain syndromes, like the pain of peripheral neuropathy, or the pain of fibromyalgia.
The only way to know if this medication will help is to try it, but I repeat, it is not used to substitute for opiate treatment, so you will most likely continue your morphine and oxycodone while trying it.
Pain management, like football, is a game of inches. If opiates lower your pain by 2 points, and you can get further pain reduction of a point from gabapentin, then your medication helps cutting your pain in half, if you're experiencing moderate (level 6) pain.
Good luck.
Talk to your doctor and/or pharmacist to be certain as everyone is different. I've tried gabapentin several times in addition to being on oxycontin and oxycodone (and some other meds at the same time.) I did find it helped with the pain but I had a bad side effect in that it made me slur my words (to the point people thought I was drunk and I don't drink.) Also, you cannot stop it cold turkey due to a seizure risk but it's not like you have withdrawals like you do with narcotics. I would also make sure you see how it affects you before driving. Lots of people have no side effects but I'm somewhat sensitive to a lot of medicines.