That's what the case normally is when someone is sick. All of the symptoms fade away. You're pretty much healthy as healthy can be.
The cough though lingers on like a bad house guest for a little while longer after everything else leaves.
Granted, the cough is not prolific as it might be doing the full stage of your illness. However it will crop up, at the most inconvenient times.
To avoid spreading your germs to others, it's ideal to cover your mouth with your sleeve. Not only do you not smother your hand with germs but you block it.
That being said, cough is the last thing to go. It's weird like that but it's true.