I would suggest going for a short easy run on Friday and see how you feel - if it feels fine, then go for it, but probably give up ideas of racing hard.........
However, if you can't breathe normally without coughing by Friday, I think I'd then accept the inevitable, and not bother with the half.......
I agree with you that runners think differently - I came down with a virus on Friday / Saturday which meant I had sore throat, cough, headache, bunged nose, etc..., but insisted on doing a long slow 12 mile run on Sunday. The run was bl**dy hard work on a course I usually enjoy, and probably contributed to the fact I then spent Monday & Tuesday off work. 
However, I decided I felt well enough to go back to work today, and if it hadn't been for my wife telling me I was being dumb, I would have done a 6 mile run as part of my commute....
GO