This is a distinction that constantly confuses, me included. I found this answer at e.notes.com which strikes me as fairly succinct. Hope you don't mind me passing your words of wisdom on!
Answer: A metaphor is typically a phrase that is used as a comparison to seemingly unrelated objects or actions. A metaphor is a rhetorical trope that represents the first subject as being similar or equal to a second object or subject in any way.
An allegory is also a representation of comparisons but on a much deeper note. An allegory typically consist of a longer passage of comparisons than just a phrase; it also includes more details than a metaphor. An allegory is usually symbolically substituted for something else. A meaningful historical/geopolitical event or a wider abstract concept is usually the goal of an allegory. Metaphors are mainly used in language, whereas allegories can be used in language, painting, sculpting, etc.
EXAMPLES OF KNOWN METAPHORS: All the World's a stage, Killing him with Kindness, Frozen with fear, My stomach was a bottomless pit.
EXAMPLES OF KNOWN ALLEGORIES:
Example #1: In the novel, Lord of the Flies it provides a compelling allegory of human nature, illustrating the three sides of the psyche through its sharply-defined main characters.
Example # 2: A symbolic representation: The blindfolded figure with scales is an allegory of justice.