As far as I know, neither of those is associated with Sjogren's. Here is a great discussion of how Sjogren's is diagnosed.
www.sjogrens.org/home/about-sjogrens/diagnosisYou are right, a rheumatologist would be the right Dr to investigate a possible Sjogren's diagnosis.
Meanwhile, you might try the Biotene line of products for mouth issues, and use an eye lubricant, such as Tears NATURALE-II, to keep your eyes moist. You want a NON-medicated eye drop that says
lubricant on the label; not anything for red eye.
Best wishes,