If you accidently hit the option in Software Update then that is an over the update (as opposed to doing it with iTunes).
The problem here is that because the update didn't complete correctly that the operating system has crashed and the iPhone has no redundancy of data or safe guards in the event of this kind of crash.
The first step would be to do a hardware reset but it sounds as though you have already attempted this without success.
Sadly, and please don't shoot the messenger, you will have no further success at this point without the ability to plug the iPhone into a computer. Unfortunately, the iPad can't stand in, either.
The only way to recover the iPhone in it's current state is to do a full restore on it, most probably using DFU mode. It will erase your Apple device, re-install the operating system, and then re-sync user data once it is done (provided you have a backup of some kind).
Make sure you have downloaded and installed the latest version of iTunes on whatever computer you can use before attempting this:http://www.apple.com/itunes/download/
(Mac users can run System Preferences > Software Update > Check now to get the latest version for their system in most cases.)
* Open iTunes on your PC and connect the Apple device directly to the computer
* Turn off the Apple device (press the sleep/wake button on the top until the device simply shuts off).
* Hold down the sleep/wake button (on the top) AND the home button (on the front) for 10 seconds
* Release the sleep/wake button but CONTINUE to hold the home button, until...
Note: When you are in DFU mode the screen will be completely black.
* iTunes should pop up and tell you it’s found a device in recovery mode, click ok and continue along for the restore.
Note: it may ask whether you wish to restore a backup from iTunes or from iCloud
. You should use which ever has the latest backup of your personal data.
Alternatively, an Apple Store or other full sevcive carrier location can run this for you, as well.
I realize this may not be teh answer you wish to hear but there is nothing you can do directly on the iPhone itself at this point given the condition it is in. If you continue to have questions on this topic, just reply back to this discussion. I will be more than happy to work with you further. Hopefully, this info will answer your question
. If so please, please remember that when you are asked to give a rating, you are rating my personal service only and not this website itself or your issue.
Thanks and good luck,