Below is a little real world experiment with one of my favorite brands of sunscreen. BlueLizard sunscreen gives great protection and the bottle turns blue when there is sufficient UV light to cause skin damage.
The first photo was taken in the car while in the garage (and the bottle is white). The second photo was taken ten minutes later after driving just a few miles in the afternoon sun (in Seattle). The bottle was never outside- the only UV light came through the drivers window. As you can see the bottle is bright blue! This means that you are getting significant UV exposure through the car window. I have done this experiment inside my home and the same thing happens. UV light passes through windows, so protect yourself and always wear your sunscreen!