I corrected my friend's pronunciation because I wanted to look clever

My friend stopped telling her story after I corrected a name she pronounced differently. I didn't just offer the correction; I repeated her version and laughed.

There were five of us at lunch. She's normally the confident storyteller, and I had been feeling like the quiet person who only supplied reactions. For once I knew something she didn't. I made sure everybody heard it.

The pronunciation itself wasn't the real issue. I wasn't helping anyone understand the story. I wanted a turn being the knowledgeable one, and I used her mistake to get it.

Would you apologize in the group, where it happened, or privately? She resumed the story after a pause, and I don't want to interrupt it a second time with a speech about my newfound self-awareness.