I bought some polarized sunglasses for my eye on the go whenever the sun is out. Honestly I don't know if i'm doing any more damage to my eyes even if I'm wearing my polarized sunglasses. The sun is facing directly at my face ( front view, side view ) and I don't know if my sunglasses are working. Especially when i'm driving, when the sun goes down and I have my sunglasses worn, I still have to block the sun although. Is it actually safe for me to just ignore the sun with my polarized sunglasses on?

I know that the sun is directly facing towards my face with my sunglasses. I try to stay away from Gradient lens because they SUCK. These aren't Gradient lens, but full polarized everywhere on the lens.
Polarized lenses essentially reduce by about 1/2 the amount of light reaching your eyes . These days they tend to have filters to reduce UV as well which is protection from cataracts. You cannnot look directly at the sun with sunglasses - it is still to powerful.

What exactly do you mean by "damage to your eyes " here? The risk of sunlight is cataracts - it has nothing to do with a need for glasses.
All polarized sunglasses will do for you

is reduce the glare, by appearing to remove the glare from object which you view.

They look "cool", but so do Ray Ban Aviator sunglasses,

which are better, and usually better for your eyes.

Never look directly into the Sun, as it is extremely dangerous to

your retinas to do so.

Being in direct sunlight, isn't the same as staring into direct sunlight. Sourse: https://lornemarrfitafter45.ca/sunglasses-can-protect-eyes/

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Alexia Wolker