1
I have a bad cough.
To sign this, point to yourself for 'I', sign 'HAVE', and then 'BAD'. Finish by tapping your 'C' hand against your chest for 'COUGH'. Make sure to use a pained or uncomfortable facial expression to emphasize that the cough is bad.
2
Please cover your mouth when you cough.
Sign 'PLEASE', then use your hand to mimic covering your mouth. Next, sign 'COUGH' by tapping your chest. This is a very visual and direct way to ask someone to be polite when they are feeling under the weather.
3
The baby is coughing a lot.
Sign 'BABY' by cradling your arms, then sign 'COUGH'. To show that the coughing is continuous or happening 'a lot', you can repeat the tapping motion on your chest more times than usual and furrow your eyebrows.