Greetings, and thank you for your question!
Certainly changing from Prozac to Cymbalta is an option. Cymbalta is good not only for depression, irritability, and anxiety, but it is also indicated for chronic pain (an ever-present companion for most with RA). You mentioned a family history of it, but not if you yopurself struggle with it. If you do, then such a switch may be a good idea.
Alternatively, you are on a very low dose of Prozac which could be increased. Given that it worked well for you, an increase to 40 or even 60 mg may get you back to feeling well. The advantage here is you know what to expect with the Prozac, and how long it took for you to notice a change.
Either option would be reasonable. I hpe this helps! Please let me know if you have any other questions, and please don't rate this until you feel your question has been answered to your satisfaction!
You are welcome, and I'm sorry you are going through so much at such a young age! Please let me know if I may be of further service.