Sounds like you tried to make a Restore, instead of an update.
If your iPhone has gone into Boot Loop, then you need to do a Restore. It will delete EVERYTHING locally from the phone. Everything stored in iCloud, contacts, photos, etc. will not be deleted, but will be retrieved when you sign in with your Apple ID.
Remember to update iTunes to the latest version. Now that your phone has failed once in an update or restore, I would recommend plugging the cable into another USB port and, if possible, try another cable.
How to make a Restore (REMEMBER! EVERYTHING will be deleted)
1. Turn off your iPhone completely
2. Connect your Lightning Cable to your PC / Mac
3. Connect the cable to your iPhone - the moment the cable is in your iPhone, press and hold the Home Button until the device enters Recovery Mode. Recovery Mode is a black screen, with a computer and a cable icon.
On your computer. Now you can select Restore. iTunes downloads new software, it may take some time depending on your internet connection. Try to keep your computer from going to sleep.