Dealing with embarrassment cause coworkers thought I threw up at a work event?

So I went out with drinks for some coworkers at a bar (most of them work remotely so it was my first time meeting many of them). At one point, I kind of choked on my beer and involuntarily spat it out.

Well, I later found out that someone saw me and thought I vomited, and they told some people. A coworker told me she’d heard I threw up and a bunch of them were worried about me. I told her what really happened, but tbh my story sounds like a cover up so I doubt she believed me… Nobody else brought it up and like I said, I doubted people would believe me, so I didn’t say anything more.

The night is over but I feel humiliated just knowing people were talking about it. Like, the truth doesn’t really matter… What people believe does. I can’t stop imagining them talking about me behind my back, shaming me for not handling my alcohol, etc… Idek if I should go to the next work function.

A couple of friends told me it’s not a huge deal but I wanna hear from others. If you were one of my coworkers, how much would you care about this? Do you have any general advice for me? Thanks!

TLDR: a coworker thought I vomited and told other coworkers and now I feel embarrassed. Want to know if this is really as big of a deal as I’m making it in my head, or if people will likely forget soon.