Can you install a iPhone up date using computer

Yes, if it has iTunes installed or is running Catalina or above. See the "Use your computer to update your iPhone, iPad, or iPod touch" section of the Related Article at the top of the page.

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you still need to free up space. the devices needs an OS to run the installer.

How to check the storage on your iPhone, iPad, and iPod touch - Apple Support

You can use a computer to update the iPhone, but the iPhone will still need to have enough free space to install the update, so you will need to free up enough space on the iPhone to handle the update.