No one will feel sorry for you, your tip average will not increase, and you will not be considered a hero for coming to work sick. Just stay home.
True, bartenders and waiters usually do not have sick pay or salaries to cover those days home from work, but that's what a savings account is for (read Chapter 11 in our book for more money management advice). There isn't a single customer who wants to see you wiping your nose or sneezing in your arm, no matter how sanitary you try to be.
Make some tea, heat some soup, and get some rest. It's the right thing to do.