He seemed annoyed when I corrected him, should I worry?

Some people get briefly irritated when they're caught out. That's normal. What matters is what comes next. Does he stay sulky for hours? Does he bring it up to make you feel bad? Does he act like you attacked him personally?

If he can shake it off in a few messages and move forward, this is just a personality quirk. People who can't handle any correction are actually the ones worth worrying about. They tend to be controlling and they'll make you feel crazy for pointing out anything factual. An annoyed reaction followed by acceptance is actually the sign of someone who can be reasoned with.

Your job is not to make his annoyance disappear. That's his to manage. What you're doing is refusing to pile on. You acknowledge what just happened without rehearsing it. You move the conversation forward like adults.

If you immediately soothe him or apologize for correcting him, you're teaching him that getting irritable is a tool that works. Next time he doesn't like something you say, he'll do it again because he learned it works. Keep it simple: acknowledge lightly if needed, then change the subject.

Don't rush to fix this. Sending something right away reads as anxious and makes the moment bigger than it is. Wait until he's had a beat to cool down. Then send something brief that moves past it.

If he doesn't reply to your next message or goes cold for a full day, that's different information. He's choosing to sulk. At that point you can decide whether his moodiness is something you want to deal with. But don't preemptively back down. Send your reply, give it space, and see if he acts like an adult about it.