Is the word whom an object pronoun?

Yes it is. The pronoun 'whom' most often functions as an object of a preposition.

The pronoun 'whom' is an interrogative pronoun and a relative pronoun.

An interrogative pronoun introduces a question.

Example: To whom do I give my completed application. (object of the preposition 'to')

A relative pronoun introduces a relative clause, a group of Words with a subject and a verb that gives information about its antecedent.

Example: The person to whom you give your application is the manager. (object of the preposition 'to')