Do you mean making yourself sick enough to vomit? Or are you talking about anxiety making you sick enough to vomit? Or are you talking "Bolimia" ei...forcing yourself to vomit for the sake of loosing weight? All three are possible problems, only due to different reasons.
Yes you can make yourself nauseous, nauseous enough to throw up, or just throw up; however, I don't know why anyone would ever want to do this to themselves. I have suffered with constant nausea that leads to vomiting for 6 years, and would do anything to stop feeling nauseated and be able to fully live my life.