I'm not sure how rare it is, but as an anecdote when I was a teen I knew a kid who had a speech impediment and slurred their words really bad/was kind of mush mouthed.

We were on a group trip for about a week and had forgot their toothpaste and had borrowed someone's 'natural toothpaste' stuff. By the end of the week they were far more intelligible in speaking and were stating it felt like they mouth deflated. They had an undiagnosed allergy to toothpaste their entire life and no one had recognized it.

The connection between canker sores and SLS is pretty well known and not rare or caused by some other allergy.

I don’t know where my parents picked up this trick, because everyone looks at me like I’m crazy when I mention it:

Relatively dry mouth. Milk of magnesia. Q-tips. Paint the sore spots with MoM. It thickens and forms a film, which cuts down on the tenderness.

I would try one spot if I were you. As bad as you described it, if that helps more than it hurts you might try gargling the stuff.