Ask your professor to allow you into the nursing lab for practice. Practice, practice, practice... maybe not so much for the skill (if you're really good at it), but to build up on your confidence.
What is making you anxious? Is it the professor's presence? The students watching you?
Those are distracters you need to learn to shut out. When you're on the floor, the patient and many times a family member will be watching you performing some of these procedures. Believe you me... they can be a lot more critical than your professor.
So it's good to build up the confidence. Your confidence will command respect and trust from those around you. You know you can do do it, so now BELIEVE it!