I also have Sjogren's and am a singer. One possibility for why you're coughing is because of the dry mouth that results from Sjogren's. Another possibility (the reason why I cough when I sing) is you could have nodules on your vocal cords. I have rheumatoid nodules on my vocal cords (though I have not officially been diagnosed with RA). Something you might want to have checked out, if it's really getting in your way.