I'm worried I look incompetent at work, what can I do?

This could be either a genuine or baseless worry. You can tell which by asking your boss honestly how you're doing at work. This person has no motivation or obligation to assure you of your competence as others might because they are your friends or your competitors. Should you find out you are lacking in some areas, you know how you can improve. You can learn from your peers, or take more courses to improve your skills. If you find out you are worrying needlessly, reflect on that discovery: it could mean you are overly self-conscious or self-critical. You can then work towards having a more healthy mental life.

I work in the ambulance service and come face to face with all sorts of unusual illnesses, issues and sometimes very high stress situations. The funny thing is that while we get plenty of training and help at the start there's no way to be prepared for everything and even the stuff you have trained for, like delivering a baby, can result in different presentations such as twins on a strangers couch. My point is that most of the time I have no idea what I'm doing. All I can do is smile, be as confident as I can and just hope that nobody can see that I'm bluffing. I then do it again and again until the point where even if I don't feel 100% confident, I'm doing a good job. That's all that matters usually, a smile, appearing confident and not completely botching the job. Everything else is a bonus :)