How can I make sure my system uses the ~/.screenrc file?

$HOME/.screenrc should be the compiled-in default. You can also specify it on the command-line:

$ screen -c ~/.screenrc

You can also set it with an environment variable:

$ export SCREENRC="~/.screenrc"

As for confirming that it's being read/used, try putting these two into your screenrc:

hardstatus on
hardstatus alwayslastline

If it comes up listing all of your windows on the bottom line, your screenrc is being read.

Brightlancer's answer is useful, but based on some limited experience I can add:

If there is an error in your .screenrc file, it appears that screen ignores the file silently.

This could explain the cause. You may like to start with an empty file and add the lines slowly to find out the offending lines.