Updating my WordPress.org version will cause my site to break… What can I do to avoid this?

As you have figured out, ‘child themes’ are very beneficial. Not updating – not a good thing.

If you have any programming skills, then you could create a child theme. (Lots of tutorials on how to do that.) Then take any page that you modified in the main theme and place them in the same folder structure in your child theme area. That should override the main theme.

Then update the main theme, and any plugins.

Note that updating the WP ‘core’ (and you should, based on recent hacks) should not affect the changes you made to your current theme.

Another alternative is to temporarily activate a new theme, then work on the child theme process for your current theme. You could also place a copy of your current theme in a different (new) folder, change the theme heading (inside the theme code) for a different name, and then activate that temp copy.

Overall, though, this is a cautionary tale about the importance of not modifying core code or themes, but to use child themes. If any of this is above your knowledge/comfort level, you may need to ask for some ($) help.