Somewhat surprisingly, perhaps, what seems to be an ungrammatical "double possessive" form is in fact more common for OP's exact context. You can't tell from the spoken version, but although no-one actually writes your's with the apostrophized Saxon genitive, we do usually pronounce the s...

Usage in respect of pronouns in coordinate possessives is a complex issue, as you'll see if you follow that link. As often happens, prescriptive grammarians tend to decisively endorse one particular usage (usually on the basis of "logic"), and dismiss alternatives as "ungrammatical". But descriptive linguists who don't have that luxury must struggle to explain why native speakers so often ignore the grammarians' pronouncements (and believe me, explaining it isn't easy! :).
So if your priority is to learn what will satisfy a pedantic exam marker, you should stick with your on the grounds that "it's already possessive". If you want to sound more like a natural native speaker, go for yours - but at all costs don't write it with an apostrophe, since this will satisfy no-one.