Contractions cause coughing?

Lorean

I am currently 32 weeks 4 days today, I have also been getting a lot more Braxton Hicks contractions. I was wondering if anybody else experiences when they get Braxton Hicks contractions, does it cause you to cough? I almost feel like when I get a contraction, my whole chest tightens up and I feel like I have to cough. Is that common?