Feeling sick during a workout can be a good thing and a bad thing. It's good because it probably means you are pushing yourself when you train. It's bad because, well, who wants to feel dizzy and nauseous?
The symptoms you have described can be caused by a couple of things...first, you may not have adequate blood glucose available, which can be easily remedied by sipping a carbohydrate drink during your workout.
More likely, however, your body is not neutralizing acid in the muscle and blood, that is produced while you are training hard. This acid buildup is a result of anaerobic metabolism, and if it is not cleared, can cause a "toxic" reaction that can lead to nausea and light-headedness.
There are several things you can do to help avoid this problem: 1) Take a little longer rest between sets to allow your body to better cope with the acid buildup 2) Take a buffering compound such as baking soda mixed in water or juice about 20 minutes before training 3) Take a few antacid tablets, like Tums, about 20 minutes prior to training.