I am on both Neurontin and Elavil....
I take the Elavil for Allodynia and Neurontin both Nerve Pain AND seizures (I also have epilepsy, but was put on Neurontin initially for the nerve pain-- as the nerve pain dosage is much less than the dosage, ironically it has help my seizures better than the pain, lol)
I would give the Neurontin some more time-- for any condition you are using it for (It took me a good while for me to see any results for either/or both conditions).
I am a little confused about your dosing, but, you mentioned you are on 600 mg right now and you've been on it 10 days. How exactly did you titrate ? And, is 600 mg your target dose or are you still in the titrating phase ? When I first started Neurontin, my target dose was 900. I started at 300 mg and increased it by 300 mg per week (some people titrate faster tho) until I reached 900 mg. HOWEVER, even if 600 mg is your target dose, it can take time to see results. Just like most of the CNS meds it takes your body a while to start building up in your blood. For example when I started Elavil (I was on Elavil before I added Neurontin to it) I titrated faster than I did with Neurontin, but it took about 3 weeks at my full dosage before I saw signifigant results. Thankfully, my doctors -- and the research I did, gave me a heads up on it.....
As for whether to ask the doctor to increase it or not is a descion only can decide. However, a lot of doctors will want you to give it a little more time unless you are having major side effects. In figuring what med would be best (least side, best relief ), I stopped Elavil (it was making me very sleepy, groggy, etc) and did trials of Pamelor and Lyrica. I was on Pamelor for about a week and Lyrica not much more--- BUT, it really had nothing to do with pain relief-- both caused severe and intolerable side effects and I wasn't able to get to my target dose. BUT, as in the case with both Elavil & Neurontin, while I had side effects, none were dangerous and i stuck with my target dose for several weeks, even though it didn't initially, signifigantly, relieve the pain I had to give it some time to see if it would help-- which it did, before we'd (my dr and I) raise the dose.
(Btw, Ironically, I had major, dangerous problems with Lyrica, but none of the dangerous side effects with Neurontin--- the complete opposite of what is most people experience (Lyrica, Neurontin's sister drug, is supposed to be the drug with much less side effects compared to Neurontin))
Good Luck and I hope you are able to get some relief soon !