You are probably not sick. Watering mouth is not the first stage. what SOMETIMES happens is that people will feel sick and when they are about to vomit their mouth will water a little and then they will vomit, it doesn't happen that your mouth waters and then you feel sick. That's just not how it works. The mouth watering is to do with the act of vomiting, so in short if you were going to be sick it would have happened.

You feel sick because you are anxious. I would bet money on that, you got yourself anxious and worked up and that resulted in a sore stomach and feeling sick because you were scared and though that way. I promise once you start relaxing and breathing it will go away. Plus you've been crying and that always makes you feel a bit blah.