Emergency iPhone Backup Option?

I'm having a lousy month (to say the least). I'm hoping I can get some good news here (pretty please!!!). On Thursday night, my iPhone 7 Plus (decked out in an Otterbox UniVerse case and with a tempered glass screen protector) fell 2' or less from my kitchen counter onto the tile floor. It fell flat on the back of the phone. No physical damage was sustained. However, the phone is completely disabled. The screen has a strange pixelation and will not respond to touch, even of varying pressure. I am receiving current updates, I receive calls, I can charge it and connect it successfully to my computer. But, again, I cannot actually interact with anything as I cannot even swipe to power off due to the screen being non-responsive. I believe the last backup of my phone to my computer was 6+ months ago, and I have an iCloud storage plan, but cannot recall the frequency of backups that I have it set to. I am worried about losing photos and videos of my children. Is there ANY way there's a master setting to force the phone to do a complete back-up on my computer or through iCloud? I attempted to back-up via iTunes, but because it needs permission to "trust" the computer from the phone, that was another dead end for me. Apple Support via phone was unable to assist. Please help! Thank you in advance for your time.