Is it normal for your work to want you to come in with the flu?

Right now I work at a grocery store as a cashier. I've had the flu twice and a cold twice (with a fever, body ache, and sweats) in the last three months. Every last employee gets sick all together within 24 hours of each other. They've only let me call off for one day in these four instances (I had to on the worst day when the virus peaked, because I couldn't stand).

I'd really prefer not to come in and spread this to all of the customers, but they don't seem to want to give me a choice. Do you all find that this is normal with your places of work?

For what's it's worth, this bout of flu that I have currently comes with vomiting, coughing, a headache, body ache, and a fever. I gave them a call, and even with the vomiting, they're saying go ahead and come in.