I need to let my son know that my phone number has changed. Can I do that by leaving a message with a corrections officer?

The easiest and most reliable way is to send it by mail. But, if you call the facility, it is 50-50 that the person answering will break their internal rules of not passing information to the inmates and do it for you. It's not a major understaking, you just have to get the right person, willing to be nice.