It is quite common to have side-effects with Neurontin. In most cases, the side-effects go away over time. It also takes weeks to months to work up to the proper dose. These side-effects will ususally stay with you during these increases, then finally settle down after a while of being at the same dose and your body adjusting to the medication. Taking it for 3 weeks isn't long enough for this process (slowly increasing to the right dose, and allowing the body to adjust).

There are many threads on Neurontin here and they might be helpful for you to read about other's experiences on this medication. There are some that cannot tolerate the side-effects, but you may have been started on too high of a dose. Talk to your doctor about your side-effects and whether an adjustment (down) in dose might be helpful (with a SLOWER increase over time).