Can I only use my computer to load the new version if it’s a Mac?

Oh, Surely.

Using iTunes, you can update software on your iPhone, iPad, or iPod.

1. Connect your device to your computer.
2. In the iTunes app on your PC, click the Device button near the top left of the iTunes window.
3. Click Summary.
4. Click Check for Update.
5. To install an available update, click Update.

Update software on iOS and iPadOS devices in iTunes on PC ...