This is one of the things that sucks about living car free. For me, biking when I am sick either helps me sweat it out and clears the phlegm out of my lungs, or it wears out my already taxed body and prolongs whatever sickness I have.
I am just finally over a nasty flu. I would have liked to pull the "too sick to bike, too sick to work" card but I am a student finishing my last quarter of college and its finals next week, so I had to suck it up and ride to school, even though i felt like ****. I had to ride home in the rain one of the days I was sick, that was terrible even though I was prepared. I had an ugly fever that night and threw up a whole bunch. I actually hopped on the bike the next morning but I was too weak to make it past downtown (~2 miles), so I gave up and took the bus instead.
I would suggest that you drive in or stay home, biking through this latest illness definitely prolonged it for me.