Will Botox work for wrinkles that are under my eye?

I have fleshy bags under my eyes. I guess they're wrinkles but they've been part of my face since childhood. The problem now is because I'm older (54) and the skin on my face has lost elasticity, they standout more and seem, if possible, bigger and full of creases. Would Botox be an effective way to treat this problem? I know it's injected around and above the eye but I'm not too familiar with its use below the eye and I'd really appreciate your opinion.

Botox can help with this, especially out to the sides, but a lower blepharoplasty (eye lift) might be a better, instant, and long-lasting result.