Try as you might and hold onto your vomit and be sure to puke while serving a meal to the customers. Then loudly state that you told your boss you were sick, he saw you puke previously, but you will lose your job if you go home sick.
Watch what happens. You will be sent home. Maybe for good. But, at least you made your point.
You cannot issue a health code violation. Only the health department can. You can, however, call the labor board and discuss how you were witnessed puking and still made to work and scheduled for a long shift the next day.
Some bosses/managers are on such a power trip, holding your job/your income in the palms of their hands and they often abuse the power. I would tell your manager's boss that you were made to stay and serve customers between times of vomiting.