Can Plastic Surgery Help my Eyes Look Less Tired?

I agree that your eyes look tired for the reasons already stated: the downward tilt of the eye as well as the low position of your upper eyelids. It is hard to say if there is true surgical eyelid ptosis, since the angle of the photograph can influence the upper eyelid position. There are drops that can be used to raise the upper eyelid margin a few millimeters. If that greatly improves the appearance of the eyes, then eyelid ptosis may need to be addressed. These drops are prescription only, so you would have to have a consultation with a physician first.
If you have true ptosis, than that can be repaired by tightening the upper eyelid retractor muscle. You may also have low lying eyebrows (more on the right than the left), which can be raised with an endoscopic brow lift. A botox brow lift may give you an idea about whether this procedure is right for you. A lateral canthopexy can help to alter the eye shape so that the lower eyelid is more horizonal.
Make sure the photograph is taken by someone else from the exact same height as your eyes and I can comment more on whether a ptosis repair is needed.
Good luck

Your eyes appear "tired" because the axis of your eyes slants downward as you go from your nose to your ear. You also may have congenital ptosis (droopiness) of your upper eyelids, with the left lid droopier than the right. I don't think a standard blepharoplasty would work well for you.
I think you should see a qualified, experienced, oculoplastic surgeon for a consultation. In the right hands, ptosis repair can open up your eyes in a straightforward fashion and help improve your appearance.
I hope this helps, and best regards.

Eyelids can look "tired" from a number of reasons. The more common ones are bags under the lower eyelids, excess skin of the upper and/or lower eyelids and drooping of the eyebrows. You don't have any of these.
Your eyelids slant downward towards the sides; the corner where the upper and lower eyelids meet (called the canthus) is lower towards your ears than near your nose. There are a number of surgical techniques that can be used to raise the lateral canthus. Sometimes, there may be some hollowness of the bone of the eye socket as well. This is also treatable. Seek out a surgeon who is versed in this procedure for a more definitive discussion.

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.