It was my periodentist that told me about Burning Mouth Syndrome. I went through all kinds of tests. It was Orofacial specialist that confirmed it. The periodentist also said that he had both men and women suffering from this goofy syndrome. Having said all this it is always possible that good ole MS can give us unusual issues. And as far as I hear and read everyone has different symptoms. And then there are the delightful side effects from the medications.
If it bugs me too much I chew a fruit flavoured gum, or brush teeth with baking soda. I also take a small amount of Clonazepam. I was told it could go into remission but it has been 4 years now. I just deal with the day. Same as with MS. Hope yours goes away.

Sorry extremely late post ... I experience this as well -- no thyroid condition no MS drugs and I am a guy so having a bit of difficultu believing this can not be an actual symptom of MS ...

I tried Amosan but could not stand it, too strong. Was prescribed Clonazepam ( mild dose) that I have been taking for more than a year and it has helped. Some days part of my lip will feel as if it is burning but it goes away.
Initially I found that either the salt water rinse or baking soda rinse helped with the burning. Now I stick to an expensive toothpaste and the Clonazepam.

Good luck. Hope you find something that works for you.

Old posting but I've been having this problem and it's a thyroid issue.

My periodentist when he heard my symptoms and checked my mouth said that I had BMS (burning mouth syndrome). It occurs to women only and those middle aged and over. Next step is to see a Dr of Oral medicine? Biogen support nurse had never heard of this but said it definitely wasn't due to Avonex. He also said it wasn't MS related. Wait until I've seen the oral med Dr.