The following is a combination of information I found on Emotional Competency and Physiology of Facial Expressions.
Fear and anxiety are closely related. Both are provoked by danger. And we all know how important danger is to a good story. Fear is the response to a specific and immediate danger. Anxiety results from a non-specific concern or threat. Translation--worry that danger is coming or will become immediate.
There are times when you will want to show your character's fear without stating it. I never thought about this before, but why do you think we make fearful expressions in the first place?
Fear expressions send a danger warning to those close by.
Synonyms for fear include: horror, fright, petrified, scared, shocked, hysterical, mortified, and terrified. The terms dread, alarm, and panic may refer to either anxiety or fear.
What does it look like?
Fear: The eyes widen and the upper lids rise, as in surprise, but the brows draw together. The lips stretch horizontally.
Body Language: See The Bookshelf Muse's page on Fear.