Yeah I've been coughing and congested pretty much this whole pregnancy, mostly asthma-related with a not-fun upper respiratory infection thrown in. I feel pretty cruddy, but the baby seems to be fine.
Cough drops are okay, Vicks also helps. I also do a couple of cups of peppermint tea with honey per day. Honey is a natural cough syrup, so you can put a spoonful in your mouth and let it melt before you swallow it. I've managed to get through without over-the-counter meds. I did have to take antibiotics for the upper respiratory infection because we were worried about pneumonia, but again, the baby is fine.
No it cannot. I had bronchitis in the beginning of my pregnancy that lasted a month. Vapor cream, Robitussin, and oral steroids were my best friends. I'm surprised they have prescribed you anything if you are sick.