All hunters, even the most experienced among us, get buck fever in varying forms. I think most hunters would agree that the excitement you feel when you spot a game animal is one of the most addicting aspects of hunting. The key is to control it long enough to focus and make a good shot. As you know, sometimes that's easier said than done. There are a few things you can do, however, to help you be as prepared as possible when the moment of truth arrives.
First, be ready for any situation you might face in the field by practicing it at the range. Removing any guesswork about judging distances, shot placement, wind judgment, etc., will go a long way toward reducing your anxiety about your shooting ability. When you start thinking about the shot and second-guessing yourself, you're only going to make things worse. If you're properly prepared, you'll be more relaxed and your instincts will take over.
Another simple trick is to try some relaxation breathing exercises. Slowly breathe in through your nose, hold it for a few seconds, and exhale through your mouth. Also, try to visualize the shot before you take it. Pick a spot on the animal's body and visualize your bullet going there. Don't look at the animal's antlers, face, or anything else except for that one spot. Visualizing and concentrating on one location will prevent your mind from wandering.
Most important is to not let your emotions get in the way of what should be a fun experience. Instead of worrying about whether you're going to make the shot, allow yourself to enjoy the moment. I think you'll find that the less pressure you put on yourself to succeed, the more success you'll have.