I had similar when I was pregnant, see your doctor as they will check that the AB script you have is appropriate (ie if it's a viral infection ABs won't do anything) and they might also be able to recommend an expectorant cough syrup which will help you get the phlegm out with a minimum of coughing. And yes you do need to rest as your immune system is suppressed during PG so your body needs to work much harder to fight the infection.

Take care.