Other Storage Increases After Deleting Apps, Photos etc

"Other" includes system files, caches, Siri voices, logs and updates - it is a common problem for this to be high, but it can often reach unreasonable levels which I presume has been the case for you and this shows some form of memory/storage corruption on your device.

Now let's get this fixed for you...

Firstly, please make sure your phone is running the latest version of iOS. You can check this by going into Settings > General > Software Update. if your phone isn't updated you should update it first because "Other" can sometimes include system updates which can be very large, and it is always recommended to have the latest version of iOS to avoid bugs and get the latest new features and security enhancements so even if this doesn't fix your issue (if you have an update downloaded but not installed it likely will) it is still worth doing.

After that, please follow the steps at  https://support.apple.com/en-gb/HT203977 before erasing my device and restoring it with that back-up which hopefully should fix that.

If you really don't want to go down that route you could try Changing Messages Settings so your messages delete sooner, by default it is set to keeping forever. Deleting your browsing data and closing down tabs on Safari also helps. If I can be of any further assistance please let me know.