You're going to be sore down there eventually regardless lol. I'm 22 weeks and baby weighs a pound and sometimes it HURTS lol she gets like in my pelvis and OW. Everything is stretching so soreness is normal. And yes, sneezing and coughing can make you sore lol. Even if you don't have coughing fits and pull a muscle, you're already tender so a cough or sneeze can yank a ligament and hurt a bit. :) It happened as early as 10 weeks for me and I worried so bad lol
Coughing makes my stomach hurt as well. But sneezing is hell!! Thats probably why it hurts in the lower region. I always lean forward to sneeze and xough. It hurts a bit less. If you go to the dr they should be able to give you something for the cough. If not just try to rest. We can take claritin while pregnant. That stuff usually works like magic for me. I know its an allergy med but it will help your sneezing.