There is actually no cure for cold and best to avoid taking medicines while pregnant especially in the 1st trimester. Even if you need to, see a dr to get those pregnancy safe meds. Do not self meditate and take any meds w/o prescriptions. It's normal to have a cold and cough during pregnancy as our body is having hormones flunctuations. Try to take a warm shower (not hot), drink lots of warm fluid, warm water + honey helps for cough, cover yourself with socks and blanket. You can also rub Vicks on your chest and rest well.
Jenny.S