You've made it this far, you should not back down. I remember having doubts up to the last minute when I took my exams. Sometimes it helps to look yourself in the mirror and remind yourself... YOU CAN DO THIS! YOU KNOW WHAT YOU NEED TO KNOW! Forget about what you know or think you know about the professors, focus on what you have control over. Prepare and make sure you have time to relax to keep your knowledge accessible.
Three weeks for three essays isn't too bad. Ours were 3, two-hour sessions over two days! Be positive, do your best, and that's all you can do. Don't worry about anything else expect for what you can control.