You can try hot tea with honey and lemon- the honey soothes your throat and the lemon cuts through the mucus. Drink tons of water as that week also thin out any mucus. Sitting in the steam from a hot shower, like mentioned above, is helpful too as is a cool mist humidifier. For over the counter remedies Mucinex works wonders and is safe for pregnancy.
Turn the shower on as hot as it goes (don't get in) and just breathe in the steam for a bit. I have the same thing going on right now and I cleared some of it out this morning.
I am 22 weeksv and I am experiencing the same thing you described. The most annoying thing is that I am scared to take any kind of meds for the coughing. I feel like a lump is sick in my throat and no matter how much I cough I can't get rid of it. Also I found that every time I cough I pee a little and I have to be wearing a pad.