Well, as a matter of fact, such kind of feeling doesn't occur too often. Personally speaking, I have never encountered that sort of experience, must be awful right? So, according to some cases, people, at least some people will have that feeling when wear glasses for the first time, feeling dizzy, wanna throw up or double vision. The reason is the lack of adaptability to the new glasses, maybe things will turn out right before long. Good luck.
In common sense, it will not cause the nauseous when you wear the new glasses. However, if your prescription of the lenses is not suitable, for example a little higher than your standard vision, you may feel dizzy when seeing things through the lenses. You should go to the eyeglasses store and let the optician have a check on your new eyeglasses.
Well, you should know that it is normal to have the situation you have described. When we wear the glasses for the first time, we have to take several days to adjust to them. Generally speaking, the most common symptoms are headaches, eye strain and nausea, and in serious situation it may extend to seeing rainbow colors and spots that are not actually there. But on the other hand, these symptoms what we have said before will usually pass with time. So it should not cause alarm. However, if more serious symptoms occur to you and they exist for a long time, I suggest you should see your optometrist at once. Or it may lead to some eye diseases.