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.
That started happening to me around 35 weeks too and unfortunately is still there and my son is 3 weeks old.