Sjogren's does not usually go into a full remission, though you may have times when you feel better than usual. My rheum describes Sjogren's as "stubborn."
Getting lots of rest, avoiding stress, eating well (you can find information about anti-inflamatory diets online), and exercising as best you can (yoga, walking, swimming) will all help, but there is no magic bullet.
As for an elevated ANA, it can mean lots of things. It is not a specific test for any one disease, even though some general practitioners still think of it as the lupus test. An elevated ANA means that--if you also have symptoms--you may have some sort of autoimmune condition. The higher the ANA, the more likely it is to be a connective tissue disease. Sjogren's is an AI connective tissue disease, and it can cause an elevated ANA. It is also possible, however, to have more than one AI condition. Your doctor will need to run further tests for more specific antibodies and will have to take your symptoms into account to determine what's really going on.