I'm having my baby on July 7th and am 38w5d pregnant. Nausea at this stage is common; there's literally no room. Acid reflux and heartburn can graduate to vomiting. I've thrown up once this week. Also it sounds like you're experiencing Braxton Hicks contractions, but it's best your doctor evaluate you.
I'm due the 7th of july also and been having the same thing go on. This is my 3rd baby and really ready for her to come out.