Hi, I've had this almost constantly, which I hope you don't, but I found some days are better than others so it's been bearable. When I had my sickness it was the worst so I can sympathise. Coughing just encourages the sickness grr. I saw a doctor a few weeks back and he advised me for excess mucus to fill a bowl with boiling water and breathe it in, Vicks added in helps if you have a cold. Also drink loads! In early pregnancy I found drinking water really difficult, but any fluids will help loosen the mucus and then it can be removed easier i.e not by coughing up and then being sick.
I hope it eases up for you, I know it's really horrible and when you are already feeling so rough, be it from fatigue or sickness, the last thing you want is this. Hope this helps x