GO SEE YOUR DOCTOR YOU SILLY BOY!
Inhaled 'all the way' and not confident you've coughed it up combined with 'feeling rough' that suggests an immune system working hard.
Go see you Doctor asap. You only get one chest full of lungs and they are pretty vital to your sport. Your choice is 'embarassment at wasting the Doctor's time' OR 'regret for the rest of your life at not going to see the Doctor'.
I'd say for a runner its a no-brainer: go see your Doctor.