Whenever I was sick or extra tired from an overtly long day at work my first wouldn't be as active. It's not always a sign the baby isn't okay. BUT if you've been sick for awhile or are concerned at all call your dr and they will give you and baby a quick check:)
And maybe something to help you feel better
You may not be able to feel them kicking because you're coughing. However lack of movement should be checked out by a doc! I say go to hospital - better to be reassured than worrying!