Facing the immigration officer is a job and a half by itself, no wonder your hands are shaking!. It seems that the best course of action would be to talk first to the doc who gave you the other medication. If you could explain the situation he could perhaps give you something to calm you down rather than slow you down and make you sleepy.
On the other hand, you could also try some self help remedies like we all do when taking exams. For example, take a cold shower before the interview, try to do something pleasant the night before, pray, or go for a walk, don't take alchohol and do not stay up late , or listen to relaxing music just before you see him etc.
Also try to think of the worst possible senario and devise alternative options. This should help you control the situation and handle it better.
Good luck and God bless