I'm guessing here but to me it sounds like reflex tears. These are not uncommon in Sjogren's and they actually happen because of eye irritation. They are the same tears that you get if something gets into your eye, etc. Our bodies produce them as a defense to wash away what ever got into our eye. It could be that your eyes are irritated more than usual and the result is reflex tears.
Dx: IBS 1989, Diverticulosis 2004, Idiopathic Acute Colitis 2006, UCTD 2007, Localized Scleroderma 2009, Raynauds 2009
Meds: Plaquenil 400mg/day, Pred 2.5 mg/day (tapering), Methotrexate 10mg/week, Hydrocodone PRN, Flexeril PRN, Fiorinal PRN, Baby aspirin, Prenatal Multi, Vit E, B12, Fish Oil, Biotin, Calcium, Folic Acid