The two are not synonymous; ‘among’ is considered less formal of the two. Books on English usage maintain that the word ‘among’ should be used when it is followed by plural countable nouns or by a word ‘indicating a separable group of people or things’: congregation, crowd, etc.
Example, The priest walked among his congregation, shaking hands with a few.
Amid, on the other hand, is mainly used with uncountable nouns. It suggests that you are surrounded by something that is usually inseparable.
Example, The three robbers escaped amid the confusion that followed the fire.