These feelings are absolutely normal, and you will learn to manage them. I got them before big job changes, before going to commanding officer positions, before heading off to OCS. Once I realized it was part of the normal cycle, I remembered to breathe and coach myself through the stress.
You will be so busy and tired in a few days, you won't have time to think about it. Thousands and thousands of people just like you jump in and get through this. USNA thinks you have everything it takes to succeed, so just decide you will.
Remember when you were little and wanted to be a grown-up, drive, do all the fun stuff adults get to do? You're an adult now, and along with the fun stuff comes the not-so-fun.
My favorite de-stress quote is below. VADM James Stockdale, USN (Ret), USNA grad and former Vietnam POW, used the writings of Epictetus and the tenets of Stoicism to get through years of torture and captivity.
"There is only one way to happiness and that is to cease worrying about things which are beyond the power of our will."
Epictetus
And, worth reading:
http://www.usna.edu/Ethics/_files/documents/Stoicism2.pdf
You can get through Plebe Summer and everything else. Take it a day at a time, or an hour, if that's what it takes to manage yourself through tough times.
Edit: And go eat donuts with the chaplains on Sunday morning!