I think it is normal, or at least common. When I hit 17 weeks or so I started having serious sleeping issues. I went 2 weeks with about 3-4 hours of sleep per night. No coughing, just tossing and turning. I suspect that I might have dust might allergies and even though I wasn't coughing, I did feel tighter at night. I got the pillow case and mattress covers and I think they have helped. I sleep better now, but I still toss and turn alot.
I think the sleeping thing is hormones. I mentioned it to my MIL and sister and they both said from the beginning of the 2nd trimester on, they barely slept. It is very common to have sleeping issues. My suggestion-get up and read something relaxing, baby books, name books, (something light and not too stimulating) watch tv, drink lavendar tea, a hot pack around my neck seemed to calm me. Get a pregnancy pillow-maybe it would help. And hope it is only temporary. With my pregnancy so far it seems like I get these things and they are annoying but they last for about 3-4 weeks and then they go away.