I am not a phlebotomist by trade. I work in an Emergency Room and a Prison. But, I put in a ton of IV's and draw a lot of blood. The only thing that I can tell you about 'what phlebotomy is like' is that it's a lot of sticking people other people don't want to stick or can't stick.
It's actually not that bad once you get confident. The thing that I learned is just to keep trying. You are going to have bad days and good days but keep going. Nobody is ever perfect.
I really thought getting stuck my self was really helpful because I really felt what patients felt. It hurts but it's not the worst pain ever.
Good luck with your class. I am sure you will like it. Plus if anything it's pretty good money.