Any time you have nausea, it could be related to at least a partial obstruction. Of course, mayo or any fat could pose a problem.
My daughter's first experience with an obstruction -- stricture in the terminal ileum -- caused nausea and vomiting, BUT she still made BMs.
The second time she flared, with the nausea and pain came pain, but much milder, because when it happened she hadn't had anything to eat for a few hours. So she skipped dinner as the flare got worse, and the nausea was worse...but it never progressed to vomiting because she didn't eat or drink anything. For two days in the hospital, she couldn't even drink few sips of water without getting nausea...treated by anti nausea medication. So she never got to the point of throwing up.
Btw, she made BMs while in the hospital, too. So yes, it is possible to have an obstruction, or partial obstruction, and still pass gas and BMs.