I'm not saying that you have speech issues, but that some neuralgias can be treated with manual therapies, and speech therapists are a good place to look for people trained in face/head/neck manual therapies. Its a disciplinary overlap.
IDK if your type of neuralgia can, but if your doctor scthink its a possibility, then its a direction to go in.
I do know that speech therapist is definitely one of the last specialists I would think to seek out for that kind of specialty. I just lucked out on my own because I was also experiencing speech issues. (It helped me regain neck movement)