To urge is to encourage someone, to push them forward to some action. To admonish is to counsel someone against some action, to advise them to not do something. So these two words are antonyms.
An antonym is a word that means the opposite of something else. So no, urge is not an antonym. It has antonyms, and it is the antonym of other words, but it is not, in itself, an antonym.