Def. get rid of SLS in toothpaste and all shampoos, etc. There's no benefit to SLS anyway -- there won't be any adverse dental effects of switching toothpastes.

But also yes go to doctor and try to rule in/out other issues.

I had this and it turns out I have a sensitivity to many toothpastes and mouthwashes. Try ones without tartar control. The very basic crest paste seems ok

My husband had this issue as a child and it has continued into adulthood. Baking soda-based toothpaste works for him. Any of the Arm and Hammer brands.