Shaky hands can be anxiety related. As for the upset stomach, you could try over-the-counter Ranitidine (Zantac) which suppresses aicd production in the stomach. Sucking on hard candy might help calm your stomach, also.

Even though you recognize that you are overly sensitive, your boss sounds toxic. I had a boss like that years ago and the best thing I did was find a new job where the environment was more supportive and nurturing. I flourished there.