You are being much too hard on yourself. I am a co-teacher in a statistics class, and I have absolutely no idea what I'm doing. But the lead teacher doesn't expect me to co-teach, and all is well. I contribute where I can. I've been up front with the class and tell them that I am learning as they learn. They appreciate it. I have been a co-teacher in Algebra I, Intermediate Algebra, Algebra II, and Geometry, and each has been a challenge. It is unfair of your supervisor and co-teacher to expect you to actually teach when it's your first time in the math classroom. Tell them that you will contribute in every way you can, but that you are just not ready to lead the class and that you hope to do it the next time you have the opportunity.

So don't quit. Speak up for yourself a little bit and relax. If I were you, I'd take a couple of sick days until you are in a better frame of mind. Best of luck to you.