Mouth pain has to be the worst thing I've encountered with MS. Mine has not stopped yet, it's improved, but I'm dealing with it daily.
Anything from mild burning up to shooting pain in my face/gums. I originally thought I may have gum disease or an infection. Turns out it's neither. Usually the right side of the mouth (top row of my gums) and in my cheek, but occasionally I get similar pain on the left side of my mouth/face.
I've had burning mouth so bad before, that it was nearly impossible to sleep. It was aggravated further by stress (before diagnosis). Not fun at all! Drinking/eating seems to calm it, even brushing my teeth, but I can't do that all day long

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Pain killers do nothing to help it either. I just have to deal with it as best as I can and try to forget about it.