Interesting topic! I wouldn't care if my t accidentally farted. Haven't the majority of us had one accidentally slip out in front of someone else? The farter gets embarrassed for a moment, the fartee quickly thinks, "omg, did she just fart?," the fart is ignored or a chuckle or two may follow along with words of reassurance from fartee to farter, story ends. Farts happen.

As for vomitting -- I would be sympathetic to her situation. I would help her clean up if needed, and would ask what she needed (water, help carrying stuff to her car, etc.) before leaving. Same as what I'd do for anyone who suddenly became sick. I'd probably follow up with her later in the day to see how she was feeling and then forget about it.