Out to Launch
This question made me wonder–would I want to send an astronaut into space who has a runny nose?
Consider this–the gradual change in pressure on a commercial flight is enough to rupture the eardrum of a congested passenger.
Can you imagine what would happen to a congested astronaut on a rocket launch into space? Commercial flights are tame relative to a rocket launch.
NASA has very strict health and physical requirements for astronauts. Their website has a section called Astronaut Selection that is worth exploring.
Although the site doesn't outline specific health requirements, I think it is safe to assume that an astronaut must be in excellent condition given the rigorous demands of the job.
If you want to learn more about becoming an astronaut, read the journal entries of from the Astronaut Class of 2004.