It's constant for me in varying degrees.

If I get a good night's sleep, I wake up and I'm good. If I'm low on the stress meter, the sensation is almost completely gone upon waking at times.

If I have stressful days, not enough sleep, or if I stay up late... the worse I'm treating my body, and the longer I remain awake, the worse the sensation gets.

Klonopin (Clonazepam) is the only medication that's helped me to dull this ridiculous pain (and it is quite painful in my case). Chewing sweet peppermint gum for me really helps too, and the pain's decreased when I'm eating/drinking.

BMS (Burning Mouth Syndrome) isn't overly common in MS, it's also very misunderstood in general, and it more often affects women, especially those going through menopause, or post menopausal.

In MS, it can be the result of damage to the brain stem, but it can also be the result of nerve damage in dentistry to put it in another context.

A very unusual symptom, but I've talked to others with MS who also share this unwelcome symptom. My neuro actually treats another MS patient with the condition as well.