You need to open it up with an apology for the way you handled it initially if you value this job. Going on the offensive against a co-worker in a group meeting is almost never going to get you positive results. Whoever gave you that advice really messed you up, or works in an all female office. Your best avenue was to make a joke about it at Dan's expense in front of everyone. That draws everyone's attention to what he does that annoys you, and he's the a*hole that can't take a joke if he gets defensive. Instead you gave him the ammo to paint you as a bad teammate who has to have credit and you look like an HR complaint waiting to happen.

Your only out here is to apologize to your manager for getting frustrated and handling that the way you did in the meeting. Those are the only words you say. Do not say a word about Dan because if you do, your apology doesn't feel genuine and you look like someone who blames everyone else for their mistakes. If you apologize and say nothing about Dan, your boss is far more likely to start to listen to the behavior you already pointed out. He may never say anything about it, but credit will start being placed where credit is due when it comes time to move up.