Can Plastic Surgery Help my Eyes Look Less Tired?

The largest component of the tired look in your eyelids is the severe downturn of the lateral portion of the lower eyelids. A canthopexy or canthoplasty should be performed to bring this portion of the eyelid up so you do not have a tired, sad-eyed appearance. The dermatochalasis that is present can certainly be addressed through both an upper and lower blepharoplasty. The primary goal for upper blepharoplasty is to remove excess skin and a little bit of fat. The primary goal for lower blepharoplasty is to remove mostly fat and occasionally a pinch of extra skin if necessary.

The medical term for the condition that you have (seen in the photo you provided) is an antimongoloid slant. This is when the outer corners of the eyelids are lower than the inner corners. (This is opposite of a mongoloid slant such as in an asian eyelid where the outer corners are higher than the inner corners). To answer your question, it is possible to raise the outer corners.
Your tired appearance may be exacerbated by droopy upper eyelids (called ptosis) which is more noticeable on your left eye. Raising the corners may be all you need, but tightening that eyelid muscled may also be beneficial. I would need to examine you in person to determine if in fact, you would benefit from that procedure as well. These are all surgeries that I routinely perform as an oculoplastic surgeon.