This is the most common side effect of gabapentin. Some say it's more common with the generic than the Neurontin, but I don't know firsthand, but it does interest me as my psychiatrist wants to try Neurontin on me next.
If this is the first time you've experienced these symptoms in the 3 months you've been on Neurontin, I would highly doubt that the med is the culprit here. The symptoms you describe could be a result of a whole lot of things. Anxiety, for one, like you mentioned, you be the cause (or a contributing factor)...a virus...a simple change in your digestive patterns, GERD ("reflux"), etc etc.
Before you "decide" that the Neurontin is to blame, go to your doctor and have an assessment. Rule out other issues first. You may even have to give it some time...to see if it is something that just simply may dissipate on its own. If you're not having any luck, then the next logical step would be to ask your doctor about tapering off the Neurontin (do NOT stop taking it abruptly) to see if the symtpoms resolve.
Good luck....let us know how you're feeling!