You will end up having to delete files, but you can transfer photos to a computer for temporary storage and then copy them back once your update is complete. You should have a look and see what it is that is taking up so much space. Settings > General > iPhone Storage will list by app. I know I was surprised by an app I had that should take up almost no data storage space and I saw it had some mysterious 2GB. I called the vendor and they had no idea what was taking up that much storage. I had to delete the app entirely to free up the space.
This support article tells you how to transfer photos and videos from your iPhone or iPad to your Mac or PC:
Transfer photos and videos from your iPhone or iPad to your Mac or PC - Apple Support
Read this support article for how to check the storage on your iPhone, iPad, and iPod touch
How to check the storage on your iPhone and iPad - Apple Support
- General article on seeing what is taking up storage on an Apple mobile device and tips on how to clear some storage space.