What your diagram indicates is a lavaliere microphone.
Most microphones of this type are omnidirectional, although some cardioid microphones are available.
I'm not sure if your project goal of isolating the cough sound means that you WANT the coughs, or you want to EXCLUDE the coughs from the dialogue....in either case, no such discrimination is possible. The microphone will capture all of the sound that is presented to it.
Placement on the wearer might help to a degree, but realistically you'll be looking at downstream processing to achieve the results you want.
Hope this helps.