Aww sayang, batuk berkahak during pregnancy is quite common because hormones affect your mucus production, tapi 4 weeks straight tu memang kena check lagi, could be allergies, post-nasal drip, or something else that needs proper management, so definitely mention it to the doctor at your pink book appointment next week. A few of my mum friends had similar issues and one swears the humidifier helped heaps, plus drinking warm honey lemon water (confirm safe in pregnancy), it's soothing and helps loosen the phlegm without the heavy medication. Since the liquid cough syrup made you nauseous, try telling your doctor that when you go; they might suggest something gentler or just recommend you ride it out with home remedies instead. Don't worry about the nurse lah, just be straightforward, tell them you've had this persistent cough and the meds didn't work, they deal with this all the time and won't judge you at all. Hang in there mama, first trimester is the toughest on the emotions!