Stephanie- respectfully I disagree and I think the OP was referring to how deep her cough sounded not that it made her seem "slob-like" or however you want to put it.
To the OP- If I am correct and you're worried about sounding like you have a deep masculine cough try not to worry about it. So did I before transition, so does my mom, so did my grandma (not blood related). So rest assured that there are many women with a deeper cough. Today I coughed and was afraid it wasn't deep enough then on my way home this guy coughed mid sentence and his deep burly talking voice let out this little cough that sounded like a 6 year old girl had coughed. I had to roll my eyes at myself for stressing at that point