I don't know how it happens, but when I update my phone, it puts all my photos from my computer, onto my phone. How do I get them off my phone? It's not as easy as it should be.

If you updated your phone by using iTunes and connecting the phone via the cable to your computer, it may have synced the photos from your computer. If so, you can remove them by using iTunes and synching again but this time change the setting on the photos page of iTunes. See the instructions below from the iTunes section of Keep your photos safely stored and up to date on all your devices - Apple Support

If you don't want the synced photos on your iPhone, iPad, or iPod touch anymore, turn off syncing in iTunes and they'll be removed from your device. You can turn off syncing for some of your photo albums or all of them at once.

Stop syncing some albums

1. Open iTunes on your computer and connect your iPhone, iPad, or iPod touch.
2. Click on the device icon in iTunes.
3. Click Photos.
4. Choose "Selected albums" and deselect the albums or collections that you want to stop syncing.
5. Click Apply.

Stop syncing all photos

1. Open iTunes on your computer and connect your iPhone, iPad, or iPod touch.
2. Click on the device icon in iTunes.
3. Click Photos.
4. Deselect "Sync Photos" then click "Remove photos."
5. Click Apply.

Learn how to delete photos and videos synced from iTunes when you can't access the originals.