Is the word my a pronoun?

Yes, the pronoun 'my' is a possessive adjective, a Word that is placed before a noun to describe that noun.

The possessive adjective 'my' is a first person pronoun, a Word that takes the place of a singular noun or pronoun for the person speaking.

A possessive adjective can describe a subjective or objective noun. Examples:

subjective: My mother will pick us up at four.

objective: I brought flowers for my mother.