Can other people tell when I'm anxious?

They can probably see it from your behavior. So if they know you and see how you behave they can tell that you are anxious.

That totally depends on the people around you. Most people might not notice unless it's a situation where you are "in the spotlight", having a presentation in front of the class, for example. But then again it really depends on the person, their empathy, their own experiences (maybe even with anxiety) etc. Some people might also think that anxious people are just shy. I imagine that close friends might notice it more often, but not necessarily everyone.