Hey, you sound absolutely normal...in fact, better than normal. Don't be fazed by those guys that don't seemed to be affected by stress, they'll be cra...erm, average pilots at best.
When I had finished my written exams, I was so depleted that I sought help from our local chemist/pharmacist. "I make this nerve tonic." he told me proudly, "Sell it to lots of students."
I took the bottle home, 2/6d it cost. One spoonful taught me the meaning of bitter. Nothing on this Earth could have prepared me for what it was like. The garden hose was about all I could think of stuffing into my mouth to make the taste go away.
Time went by. I was now a Co-pilot with a good airline out of LHR. Things were great, and I was home with the old gang. In a moment of mischief, I poured the nerve tonic into an empty Bolls stone bottle. About 15 of the 30 people in the room had a snort. To this day, the image of their faces stays with me...some of them have even forgiven me. Well, they say they have.
These courses are designed to make you feel terrible. Just ride with it, and look forward to the day that you're flying a shiny new bird. It'll happen, and the more you care, the better pilot you'll be.