hello, it is very difficult to comment what can be causing the pain without detailed history and examination. from what you say, she is likely to be having pain due to nerve compression if you say that is a shoot pain down the arm. but ofcourse if there is pain on pressing the hand then joint or muscle inflammation needs to be seen. if she is a diagnosed case of sjorgren then joint pain is likely. she needs a thorough check up by a internist or a rheumatologist. Fluoxetine takes taleast 6 weeks to act. Fibromyalgia causes wide spread body pain, so, although she might have fibromyalgia i doubt if that is causing the shoulder pain.
Next Steps
consult a rheumatologist for correct evaluation of shoulder pain and hand pain( wwhether its joints) or she is having nerve compression. bith conditions can be controlled.
Health Tips
if her pain gets better with activity then you can try hot fomentation of the joints and muscles of the concerned arm. that might relive some pain.