Are who and whom personal pronouns?

No, the pronouns 'who' (subjective) and 'whom' (objective) function as both an interrogative pronoun and a relative pronoun.

• An interrogative pronoun introduces a question.
• A relative pronoun introduces a relative clause, a group of Words with a subject and a verb that tells more about the antecedent but is not a complete sentence.

Examples:

interrogative pronoun: Who is the new math teacher?

relative pronoun: To whom do I give my completed application.