That started happening to me around 35 weeks too and unfortunately is still there and my son is 3 weeks old.
It all depends on your body. Everyone is different. I was sicker than sick in my 1st trimester, it went away completely in the 2nd, and then came back halfway through my 3rd. Right around 35 weeks also. I got really nauseous and puked a few times. However mine is sporadic. Some days I feel great, and others I feel so nauseous that I can't eat, even water makes me nauseous on the bad days. My doc prescribed me zofran, and it helps but I don't like to take it very much. Just don't like the idea of taking medicine if I can avoid it. Good luck. Hopefully it doesn't last the rest of your pregnancy.