Have you considered that you might have a zinc deficiency?” Zinc. Zinc is an essential mineral that's vital to your health. In fact, a deficiency in zinc may impair skin health, digestion, immune function, reproductive health, and growth and development ( 6 ). It can also cause chapped lips, as well as dryness, irritation, and inflammation on the sides of your mouth”. If you do decide to take Zinc you also need to take copper.

Shortly after I was diagnosed with Sjogren's I developed an allergy to SLS - sodium lauryl sulfate - an ingredient in most toothpastes. It looks like an extreme version of Sjogren's dry mouth. Once I started using toothpaste without SLS my Sjogren's mouth symptoms became much more manageable. Sensodyne's Fresh Mint doesn't have it and I think Tom's is SLS free.
You might try changing your toothpaste. My dentist is the person who suggested this remedy. Hope this helps.

I blend aloe Vera in my protein shakes. For my skin, especially due to the cold season.