Can.anxiety simply go away?

Yes: There are many types of anxiety, some anxiety conditions tend to be chronic, others can be transient or episodic (they come and go).

Yes: Some forms of anxiety are temporary and situational only. This could go away on its own, especially after the problem producing or contributing to anxiety is resolved. Other kinds of anxiety are more chronic and most likely need treatment -- such as panic disorder, generalized anxiety disorder, post-traumatic stress disorder, etc.

Assess consequences: Important to know that anxiety can go away, especially by itself. Also important to ask if it has negative consequences - this should guide your decision to seek an evaluation.