Hello, During the first trimester, Tylenol (paracetamol) is the safest analgesic (pain killer). You take a slightly higher dose about 1000mg once or twice. But taking any other analgesic is not good in this period. Please check with your local doctor as to why cough is occurring. If there is respiratory tract infection like pharyngo-laryngitis along with throat (tonsil) infection, you may need some safe antibiotic to overcome the infection and cough. Usually cough take a bit longer to recover. Thanks.