Will I die from sjögren’s syndrome?

No. Sjogren's does give you a somewhat increased risk of malignant lymphoma, and it may run with a disease like lupus or scleroderma which you'd know by now whether or not you have. By itself, sjogren's is a nuisance disease. The most dangerous feature is that maybe 1% of patients get a vasculitis that can cause brain dysfunction that mimics multiple sclerosis. Be alert as it's manageable.
Possible, but unlikl. Possible but unlikely, dependent upon complications. Simply having DX may only need observation or minor meds.