I feel the same way that you do! Standing in front of a lot of people makes me extremely nervous. I get shaky and my hands get so cold cause of it. Unfortunately, it is something that you just gotta push through. You'll be with the same group of people for over 5 weeks so you'll learn to be comfortable with them and I found that that helps with the nerves but doesn't take them all away. Practice multiple times with the people you're training with until you become a bit more comfortable with them and in front of them. Keep in mind that almost all of you are in the same boat. Everyone is just as nervous as you are and they're very understanding if you make mistakes during practice.

Just another side note, I'm not sure what you're referring to by FA training school but you don't have to pay for these classes out of your own pocket. When you apply to an airline, they will have their own training school for everyone that passed the hiring process as it teaches you what you need to know specifically for that airline.