3 Answers

I wouldn't. It's mainly used for seizures. Is this your medication or someone else? Here are some facts that I found:  Gabapentin is used primarily for the treatment of seizures, neuropathic pain, and hot flashes.[1] There are, however, concerns regarding the quality of the research on its use to treat migraines, bipolar disorders, and pain.[2]

Pain

Gabapentin provides significant pain relief in about a third of people who take it for fibromyalgia or chronic neuropathic pain.[3] It is also effective in reducing narcotic usage post operatively[4] and is helpful in neuropathic pain due to cancer.[5] It has not been shown to be useful for HIV associated sensory neuropathy.[6] When used for neuropathic pain it does not appear superior to carbamazepine.[7] Further evidence is needed to determine if it is effective for migraine prevention.[8] It appears to be equally effective as pregabalin and is of lower cost.[9] It does not appear to be of benefit in treating complex regional pain syndrome.[10]

Seizures

Gabapentin is approved for treatment of focal seizures in a number of countries[11] and evidence supports its use for treating partial and mixed seizure disorders however there is insufficient evidence for its use in generalized epilepsy.[12] There is little data to support its initial use over older anticonvulsant medication for any type of seizure disorder.[13]

Other

There is some evidence of benefit in acquired pendular nystagmus and infantile nystagmus but not in periodic alternating nystagmus.[14][15] Gabapentin may help with menopausal symptoms.[16][17] It may be effective in reducing pain and spasticity in multiple sclerosis.[18] Gabapentin is not supported for alcohol withdrawal,[19] and treatment of smoking cessation have had mixed results.[20][21]

Negative

Gabapentin has been prescribed in the mental health context. Numerous trials show that it is not effective alone as a mood-stabilizing treatment for bipolar disorder and so has no therapeutic advantage in having fewer side-effects over better established bipolar drugs such as lithium and valproic acid. Gabapentin is useful in the treatment of anxiety associated with bipolar disorder, but has limited usefulness in disorders such as social anxiety disorder and obsessive-compulsive disorder, in treatment-resistant depression, and for insomnia.[22][23]

A double blind, randomized controlled trial found gabapentin ineffective for the treatment of idiopathic subjective tinnitus.[24]

Adverse effects

Only if your tooth pain is nerve related such as Trigeminal neauralgia.Your doctor or dentist can advise, for your sake i hope you only have a cavity and not Trigeminal neauralgia.

Gabapentin is not a typical tooth achemedication. It is used for treatment of chronic neuropathic or pains associated with fibromyaglia. I think you should go to a good dentist who will prescribe you with the medication that fits you, be it Gabapentin or not.