Can I back my phone up with out being hooked to WI-FI

For information about backing up to iCloud using cellular data, see the following from: Back up iPhone - Apple Support

Note: On models that support 5G, your carrier may give you the option to back up iPhone using your cellular network. Go to Settings > [your name] > iCloud > iCloud Backup, then turn on or off Backup Over Cellular.

Another option to backup without wi-fi would be to backup to a computer. See: How to back up your iPhone, iPad, and iPod touch - Apple Support