Why do bright lights hurt my eyes even when I'm wearing polarized sunglasses?

Photophobia. Because polarization doesn't decrease brightness. You need a stronger tint.
Very sensitive. Polarization tends to cut glare but total brightness may still pose a problem in high intensity situations such as watersports or skiing. Having a darker lens, sometimes mirrored with polarization should provide the most comfort. If the eye sensitivity started acutely with a red eye you should be checked out for iritis.