did you make a nandroid backup before your update? If no then here is the problem and solution that I faced recently.
On my Walton primo g1(a local branded phone manufacturer is Gionee) I got an update from 4.0.3 to 4.1.1. So as-usual I decided to update my phone. But after updating my phone I faced frequent crash and had to reset my phone to update it again. However, after this time whenever, I went to market to download anything it prompted the low device storage message. Even I am using my browser and surfing on net, it freezes and gave me a notification that low memory on device. So I looked into my device storage and found only 13 mb were free on my rom.
So, I decided to root my phone and to use a custom rom. But after rooting when I went to root/data/data file path, I found all those apps data that I installed previously on ICS rom are still there, which is about 350mb (internal space 500mb and 412mb is user available on my phone). So, I just went to CWM and did wipe data+wipe cache+wipe delvic cache and re-flashed the rom. And my problem was gone.
I don't know about your case here, but it seemed way like my problem. So, you can also give that a try. Just wipe data,cache and delvic memory and flash your phone with the stock JB(which you can download from the samsung website) rom again with odin. And this should fix your issue.
Hope that helps