I had the same worry when I was pregnant, and honestly the abdominal soreness from coughing can feel quite scary but it's usually just your ligaments and muscles stretching as everything shifts. That said, the persistent coughing itself is worth getting checked out with your gynae or PD polyclinic just to be safe, especially since the cough mixture isn't helping and you want to know what's safe to take during the first trimester. Your baby is well protected, but getting proper advice will give you peace of mind and help you get relief faster.