I took cough meds as prescribed to me when I just confirmed my pregnancy at around 4 weeks because I was down with covid. Like you, I was really fearful of tetratogens (anything that may result in foetal developmental issues), so I was wary of taking the cough syrup, and took only sparingly, really to ease the cough especially at night. I also took the cough drops sparingly when I have to get relief. Mostly, I drank warm water, lemon water, honey to try and help my recovery. I'm still coughing even though one month has passed, and the cough will get better with time..
I read that coughing doesn't affect the baby, so try not to worry too much about that! It's important to treat the virus or bacteria causing your immune system to go out of whack though, so concentrate on getting better, and if you must medicate, just take. Hope this helps, and get well soon!
Nur Nahari