I recently designed a rack for a car, but it is ve...

Avoid any counter-bores or sharp voids perpendicular to the airflow. If you have any, you might easily find your problem with a simple test drive and some clay. You can then proceed in designing ways to plug the areas.

Whistling sounds can also be created by pressure fluctuations near trailing edges, which then interact with body panels.

These types of design issues are not always intuitive, since you really need the ability to evaluate velocity contours/vector field maps along with sound pressure level maps, to fully evaluate the design. FLUENT would be a great tool, if you have access to it.

Other than that, you are left with drive-and-test options, but I would check for the usual suspects first. Some reading on antenna, outside rear-view mirror, window wipers, etc., will give you some ideas of typical issues associated with their design both aerodynamically and in terms of NVH.