It may sound crass, but one of the most valuable piece of advice I received as a new guy was that YOU are not the one having the issues. You have the training, you have the knowledge, and eventually you will also have the experience. As was said above, you need to be confident and competent. People called YOU because they cannot handle whatever their problem happens to be. Trust yourself, trust your training, and always review to stay sharp- especially with issues you may not see very often.
Focus on the basics- regardless of how messy a trauma is, or how complicated a very sick patient;s condition may be, you always start with your ABC's. You need to look beyond the blood and gore on a trauma, and beyond the fact that a person may be a diabetic, COPD, extensive cardiac history, and a dialysis patient. Airway, breathing, circulation, disability- establish the basic parameters, treat as appropriate, and move on from there. One step at a time keeps you focused and ensures you do not get tunnel vision and miss something.
You will never completely lose that anxiety- and honestly, you never really want to. That twinge of anxiety keeps you focused, and the adrenaline rush is one of the best things about the job. Even after 30+ years, I occasionally see something "new" and have a momentary "Uh oh", moment. Most often, these moments happen when you get complacent- you assume a call will be routine and something strange happens, or a 20 year old with abdominal pain turns out to be multiple stab wounds with a sucking chest wound(actually happened to me.)
You get over the momentary shock, and simply do your job. For most, the best part of the profession is you never know what to expect- most of us do not want to fly a desk in a routine 9-5 job.