Saw on Facebook that a friend I had a falling out with 2 yrs. ago just had a baby, so I sent a message of congratulations. She didn't reply, but should I keep reaching out?

Before social media this kind of information was restricted to catch up chats with a mutual friend you at lunch or over the phone. It was much easier to allow people to float in and out of your life because their photos and major life milestones weren't being broadcast. Let's remember that it's also normal to lose touch with people whether or not there's been a falling out.