Is it true that botox injections relieve vulvar pain?

Botox. If you have painful intercourse or vulvar muscle spasm as the source of your discomfort then ,yes Botox may help relieve that pain. Talk to your Gyn or plastic surgeon.
Maybe. If you are suffering from vaginsmus, ie uncontrollable painful vaginal contractions, then Botox could theoretically help. Totally external pain, such as vulvodynia, which is pain isolated to the vulva is probably not going to get better with botox.
Not usually. Botulinum toxins are used to temporarily relax muscles-particularly the ones that cause eye and face twitches; neck spasm; TMJ & even migraine headaches, plus cosmetic uses for facial, neck and chest muscles and excess sweating of the armpits, hands and feet. Btx has been used off-label for relaxing the anal sphincter for patients with spasm from hemorrhoids and fissures though.