You must decide which whistle occurred first. If your partner's whistle was first, you must ignore your whistle, unless you decide the contact was intentional (possible) or flagrant (unlikely).
If you decide your partner's whistle was first, and the contact was not intentional, some might have you call any minor transgression against the offender on your whistle the next time it happens (basketball's version of the FYC). I can't recommend that, though, because it's against the rules.
