Anxiety CAN be a side effect of Cymbalta:
http://www.webmd.com/drugs/drug-91491-Cymbalta+Oral.aspx?drugid=91491&drugname=Cymbalta+Oral&pagenumber=6
SSRI's/SSNRI's are used to treat anxiety/panic (among many other things, including pain), but the side effects can INCLUDE anxiety/panic (sounds so counter productive, doesn't it?). I think that sometimes the anxiety will go away as your body gets used to the drug. Also, some docs will prescribe an anti-anxiety med to use with the SSRI/SSNRI initially.
A few years ago I had the worst panic attack of my life after taking Celexa (an SSRI). I had problems for days. I stopped the Celexa and ended up taking Zoloft for a short period of time, which didn't seem to cause the same problems.
So, I guess what I'm trying to say is that SSRI's/SSNRI's definitely can trigger or worsen anxiety/panic. That often calms down with time and/or a change to a different medication. I don't know if it was the Cymbalta or not, but for your doctor to say that it definitely wasn't is disingenuous in my opinion.
It doesn't really help the fibro if it causes panic.
I hope you are able to find a doctor who will work with you, and I hope you feel better soon.