Is the word our a personal pronoun?

No, the pronoun 'our' is a possessive adjective, a Word placed before a noun to describe that noun as belonging to the speaker and one or more other people. The possessive adjective 'our' is a first person, plural pronoun.

A personal pronoun is a Word that takes the place of a noun for a specific person or thing. The first person, plural personal pronouns are we as a subject and us as an object in a sentence.

Examples:

Jack and I are planning our vacation. (the possessive adjective 'our' describes the noun 'vacation' as belonging to Jack and the speaker)

We went to the beach last year. It was a lot of fun for us. (the personal pronoun 'we' takes the place of Jack and the speaker as the subject of the sentence; the pronoun 'us' is the object of the preposition 'for')