What's a good way to handle this situation with my boss?

I have bronchitis and am coughing my lungs out and have a stuffy nose and I sound like an 80 year old man with emphysema. I wouldn’t want me making my drinks at work, but I have an 8 and a half hour shift in an hour. I couldn’t get a hold of my boss and no one can cover for me. Should I just have an intense coughing fit in the car before I go in and then try not to breathe for the rest of the time? Or ask to go home a little early? I hate asking off for sickness. I don’t even like asking when I can have my lunch break because I feel pushy.