Kelly,
I have that, too, and it annoys the heck out of me. I wouldn't think it's the Neurontin. I've been on that for 2 yrs now, and my twitching/jerking began about 7 months ago. When my calves start, I tell my DH, "the babies in my legs woke up." It feels the way my abdomen did when I carried the kids. I first got it in my calves, then my thighs, now my arms, too. I don't mind that as much as the spasms; those hurt like heck.
I guess stretching would be advised. The problem is when it wakes you up...don't know what you could do about that.

Take care, and hope your twitching dissipates soon.