I learned about this many years ago and the difference after I started using only SLS-free toothpaste was night and day. I used to get canker sores (mouth ulcers) any time I would bite the inside of my cheek, hit my gums with the hard parts of my toothbrush, etc., and this completely stopped a while after I switched to SLS-free.
SLS is Sodium Lauryl Sulfate, by the way, and it’s a detergent. From what I understand, the only reason why it’s added to toothpaste is to make more foam when you brush. But the SLS-free toothpaste I use makes plenty of foam, so I have no idea why they add it. It’s one of those things about the modern world that makes absolutely no sense. The ads and packaging should say in big letters: “now with even more canker sores!”
Unfortunately, the vast majority of toothpastes on the market (at least in the US) have SLS. I can only seem to find SLS-free toothpaste in natural food/supplement stores. It’s extra difficult to find toothpastes that are SLS-free but that keep fluoride too. The difficulty (and price? I haven’t compared) is completely worth it to me though.
TL;DR: The SLS (Sodium Lauryl Sulfate) in most toothpastes is unnecessary and (edit: CAN cause) canker sores (painful sores in your mouth and gums). If you have this problem, you will likely benefit from SLS-free toothpaste (some still include fluoride) that you can usually find at natural food stores.
It’s very possible. That stuff seems to wreak havoc on the mucous membranes in your mouth. It sounds like some Sensodyne toothpastes are SLS-free, so that would be easy to try.