Q: Help! Nothing is working

Phone crashed, all of my pics and videos "deleted" but it still shows they are there when I look at my storage. I needed to upgrade to iOS 10 anyway so plugged it in to my laptop. I haven't backed it up in awhile so attempted that but kept getting the corrupt errors (assuming because of iOS). So I chose to forego the backup for the moment and just download iOS 10.

This is when it gets weird. I had COMPLETELY cleared everything but pics off my phone because I cant access them due to what I stated above. I had 1.7GB available on my phone (which already seemed strange as it says I have 7GB more in storage than I actually do) and now with nothing but the factory apps it says I have 14mb available and I need 770mb for iOS 10 to install. I am literally watching the available space tick down. What do I do? There is nothing more I can delete and I really don't want to lose 18GB of pics and videos of my toddler.