I've been in the exact same boat the entire time Since I got my bfp so I feel your pain and can tell you exactly what pharmacists and dr said to me !
Unfortunately not a tonne you can do. They said regular tylonel is fine - not tylonel cold or nighttime tylonel or any of that . They said no cough syrup. Honey and lemon like a lot of girls here have said, the warm honey drink is great. They also make cough drops that are 99% honey, they cost a bit more but you're not worried about all the chemicals in the other cough drops that way. They sell them at shoppers and London drugs depending on where you live, I don't know if you have those stores, probably not London drugs anyway. Anyway, get lots of sleep and drink tonnes of water.
My cough did not go away , I know you don't have a bad cough, but if it turns into what I had then go to the dr. He ended up giving me a prescription for an inhaler, which is also safe, it just goes into the lungs . And that's the only thing that had allowed me to breath properly again. After six weeks my cough is finally starting to go away.