Is your considered a noun determiner?

Yes, the Word 'your' is a pronoun, a possessive adjective, which is a determiner.

The pronoun determiners are:

Possessive adjectives: my, your, his, her, their, its.

Demonstrative pronouns: this, that, these, those.

Numeral pronouns: some, any, few, many, none, all.

Distributive pronouns:each, either, none, neither.