I also graduated in December, and went to the CVICU right after school. I knew it would be hard, but we did a rotation there as students and I LOVED it, begged for a job, and I got it.
Some nights I still feel sick going to work... so you are not alone! Although I am not getting fresh open heart patients yet (that happens at the one year mark), I still feel overwhelmed at work some nights... I guess most nights. However, I feel like I'm learning like crazy... from the drips to what to do in different situations. I have completely grown in the environment, and quite honestly I think it's hard not to.
I know the way of thinking was for new grads and "inexperienced" RNs to start on a med/surg floor to learn organizational skills, etc. We are getting cancelled so often now that I have been floating to medical floors and the medical ICU. I think all areas are different, and you will take the skills you learned on med/surg to wherever you go. I think the ICU just gives me more confidence, because I feel as if I am competent enough to man any situation. It's hard for me to say if I would feel that on another floor or unit, because this is what I am used to. Just know that the ICU is challenging, but you are never alone in a situation. I am constantly asking questions and having people help me with tons of stuff... I never feel like I am stuck doing something by myself. I think it's really important that you not only find a place where you feel comfortable in your nursing skills, but also with the people you work with. That's what makes it all worthwhile ya know?
But go for it! I can tell you that from my floating experiences to other units, I definitly prefer the ICU. It keeps you on your toes and you are constantly learning. You can do it!