Hum that is a strange issue. What app were you updating if you don’t mind me asking? Perhaps that app didn’t like jellybeans as much as I do

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First of all when installing or updating apps I recommend you leave your WiFi ON, that way you don’t use up your cellular data and it’s most likely faster depending on your wireless internet speed.
Less chance of it hanging or freezing up on the installation for hours, but if you have good signal strength it should have still updated.
Rooting (in my humble opinion) is a LAST resort. Some Wireless companies might consider a rooted phones warranty void. But since you were simply upgrading something the issues is probably software related.
Here is what I recommend you do.
Backup your phone (contacts, pictures, messages, etc) but NOT your apps. (you can still write them down just don’t save them to your SD card if you have one).
Factory Data Reset the unit. This will (as you know) set the phone to its default settings and should fix any bugs.
Note: right before you do the reset you might see a “backup my data” and a “Automatic Restore” option. Make sure you UNCHECK the “Automatic Restore” option (you can leave backup my data checked if you want to).
Make sure you backup your info first. A reset will probably fix it. Oh and WAIT a few days before downloading apps again. Just to rule out an app as the culprit. After a few days if everything’s working fine then start downloading apps but one at a time. If you download an app and your phone starts acting up then uninstall the app and if it’s still acting up perform the factory data reset.
Let us know what happened.
~James