The cough response is usually from sinus dripping down your throat and you need to clear your breathing passage.
One teaspoon of salt for canning and baking or pure sea salt in a quart of distilled water is the recipe for relief! You can sniff it up your nose over the sink, use a neti pot, or an eye dropper to get it to the targeted area, sinuses.
This usually stops a bad cough in its tracks, and can actually cure a sinus infection faster and better than antibiotics, without the nasty side effects of antibiotics.
This would be the number one remedy for coughs and colds in the world if it was fun to do! But, it has zero side effects and the only thing that could possibly go wrong is if you accidentally drowned yourself! Lol For you and the baby, give this a try.
When I tell a doctor that is what I use for my sinus and cough problems, they always get a smile on their faces and tell me how good it is for the problem, my lung specialist for my asthma was genuinely enthusiastic! They are always surprised at patients that don't want a quick fix antibiotic for the sniffles and hangnails, or worse yet (if possible), steroids. They don't take that stuff themselves but they didn't know they had a patient somewhere that was as smart as they are about safe cures for common problems!