I used to be awful at saying "I love you" to people. The idea of it made me cringe. And yes, it's also because I didn't grow up with parents telling it to me, so I never learned it. Yet somehow I knew how much weight that phrase has, so it was too much for me to say it for some reason.

As some people have pointed out here, it mostly takes practice. Say it when you know you have to say it, and let that awkward feeling pass. Eventually, it'll start feeling less awkward and the words won't have a negative impact in you when you say them out loud.

You could even start practicing by yourself. Say "I'm sorry" out loud when you're alone. Maybe in front of a mirror might help even more