To even consider a backup you'll need to get it working at least temporarily:
If your iPhone won't turn on or is frozen, click here --> https://support.apple.com/HT201412
If your iOS or iPadOS device restarts or displays the Apple logo or a spinning gear unexpectedly, click here --> https://support.apple.com/HT203899
Once you can get it started:
To learn "How to back up your iPhone, iPad, and iPod touch" click here --> https://support.apple.com/HT203977
Note that a backup and restore is all or nothing, so if you restore from a backup you might just be back where you started. You need to get rid of stuff:
How to check the storage on your iPhone, iPad, and iPod touch
https://support.apple.com/HT201656
- General article on seeing what is taking up storage on an Apple mobile device and tips on how to clear some storage space.
How to Free up space on your iPhone [Apple YouTube video] --> https://www.youtube.com/watch?v=bnhuHSv_WrI
Note there's different kinds of "storage". Click on this link to "Learn the difference between your device and iCloud storage, ways to manage your space" and upgrading to iCloud+ if you need more --> https://support.apple.com/HT206504
If you can't back up to iCloud, click here --> https://support.apple.com/HT203516
If restore from iCloud backup failed, click here --> https://support.apple.com/HT212201
Manage your photo and video storage --> https://support.apple.com/HT205703