“Other increases in size when anything is deleted, preventing me from creating more storage”

My iPhone’s storage is full. I’ve deleted all possible apps, my photos are not in my phone anymore, and I’ve deleted numerous text messages. You’d think I’d have free space by now, but I DON’T! Every time something is deleted, the “other” section gobbles up more space preventing my phone to save anything.

How do I fix this problem WITHOUT buying a new phone.