HELP! S3 in boot loop after failed firmware upgrade

[heat618]

So yesterday I received a message that there was a system update that needed to download on my phone. I hit start on the update, and shortly after realized that I probably didn't have enough free space on the phone to install the update. I had maybe 550 MB free. the update went through its download cycle and when rebooting, i noticed a new Verizon and Samsung splash screen, but then the phone kept rebooting, over and over without ever fully booting up. I went into recovery mode and cleared cache and restarted. No fix. I tried it again and cleared cache twice and it booted up finally. I was able to use the phone all last night and part of today. I some music from my phone to make room for new music, but ended up with more free space than when I started. I did that this afternoon and went to make a call right after and my phone restarted on its own and is now in the boot loop again, this time without a verizone and samsung splash screen, but I still see the galaxy sIII splash screen. I've tried clearing cache again, but that doesn't do anything. I REALLY don't want to factory reset it as that will erase all the data on my phone and I have not backed anything up. Is there anything else that might fix this problem?