Don't worry. I finished RN school this last December, and JUST passed my nursing boards (NCLEX). I'm a 38 year old male, I work on an Adult Step-down unit (not sick enough to be in the ICU, but not well enough to be on the floor. An "in-betweener" if you will (grin). )
Plenty of jitters to come, but you will get through it. And don't let the gagging thing get you. I was a paramedic for years, and for some reason, when someone puked, I puked too (I kid you not. Once, when we just entered the door of a lady who was busy having her heart attack, -her daughter opened the door, we went through, she was on her couch in the living room, right next to the door. She threw-up, I looked at my partner, told him to get her on O2 15 liters, non-rebreather, hook her up to the monitor (what I said was "Set her up!" -which meant all of the above for this type of call) and I ducked right back out the door, threw up in the bush next to the door, then went back in and got to work. It was me. Earned me a bit of ribbing, but hey, thats the way I was).
Nowdays I don't get that way anymore (dunno what changed). My point? Don't let that stop you.
As for the IVs, if you miss the vein, then you will try again. You will miss a lot of veins over the years -don't sweat it. Even the best, will have "off days". It takes practice.
Ari, congrats on getting done with the program! Good luck on your boards test. Getting through this stuff, is a wonderful feeling!