Is us a third person personal pronoun?

No, the personal pronoun 'us' is the firstperson, plural, objective form.

The pronoun 'us' takes the place of a noun or pronoun for the speaker and one or more other people as the object of a verb or a preposition. Example:

Josh, Jane, and I went to see our grandma. Grandma made lunch for us.

The corresponding first person pronoun that functions as the subject of a sentence or a clause is 'we'. Example:

We went to see our Grandma. Grandma made lunch for us.