Plain glass only stops UVB rays, which commonly cause sunburn on the surface of the skin. However, glass does not stop UVA rays, which penetrate deeper into the skin and which cause much more skin damage.
Anyone who has lived for extended periods in a hot sunny climate, such as Outback Australia, or the Middle East, or any similar climatic region, knows full well that you can get sunburnt through untinted glass.
You would be well advised to use SPF30 rated sunscreen on exposed skin, or carry some tinted material that you can position between you and the sun, on the window.