Iphone Froze in Apple logo

Hi, I was doing a back up of my iPhone and out of nowhere my phone turned off and the screen was left with the Apple logo. I looked for what to do online and I did it but it didn't turn on, I tried to connect it on my computer when a sign of restore appeared and it let me try to update the phone to see if it turns on but in the middle of downloading the software the connection seems to be cut off and it stops. I went to Apple today and they couldn't do anything because if they connect my cell phone to their computer and try to do the updating thing and it doesn't work, my cell phone is restored and I lose everything. The issue is that I have not made any backup of this cell phone and that is what I was doing yesterday.