Can Any Surgery Fix my Asymmetrical Eyes?

Your eyes are asymmetric because your right eyeball (globe) is more prominent than the left and your left eye is lower than the right. This has to do with how the eyeball sits in the eye bone.
Differences such as these are normal and do not warrant surgery. I am sorry they cause you so much distress.
In cases where eye asymmetry is significant, camouflage procedures can be done, to adjust position of the lower or upper eyelids, but greater variations would have to be present.

There are multiple anatomic abnormalities that can result in asymmetry of the eyes and face. These may include deformities of the orbital bones, eyelids and eyebrows. In most cases, they are relatively minor, but in some cases, they may be severe and extremely noticeable. Depending upon the deformity, treatment may or may not be possible.Although it's hard to know exactly what's going on from your history, I suspect you have boney orbital asymmetry. This is confirmed by your history of an enlarged right cheekbone and eye.Asymmetry of the facial bones can be a major contributor to facial asymmetry. When this occurs, it's not unusual to have one side of the face that has a depressed orbital rim and flattened cheekbone and an eye that appears smaller than the opposite eye. These findings are often related to a condition called plagiocephaly.Unfortunately, it's not possible to correct this type of deformity without major surgery upon the facial skeleton. This type of surgery wouldn't be justified for a relatively minor deformity.If you're concerned about facial asymmetry, it's reasonable to consult a  board certified plastic surgeon. This surgeon should be able to address your concerns and alleviate your anxiety.

Thanks for the picture. I can appreciate some differences in your eye shape. Periorbital surgery could be helpful depending on the nature of the problem. The problem could range from issues with your brow, the orbital/cheek skeleton, position and function of the upper eyelid just to name a few. Periorbital surgery is sophisticated surgery if done correctly and to deliver consistent results. You should visit several plastic surgeon with expertise in periorbital surgery. I hope this is helpful.
Dr.ES

In addition to the findings discussed by the other physicians, it is also possible that you may have bony conditions which contribute to the observed appearance. These are not typically corrected unless they are severe.

Unfortunately, it is impossible to know what is happening in regard to your eyes from a flat one dimensional photo. It appears not that one eye is larger (globe) but the fact that you have ptosis (drooping eyelid) on the left side makes your eye on the right appear larger.
This is very common and can be fixed surgically. If the right eye truly is more prominent other disease processes need to be ruled out including thyroid disease. You are best to be evaluated by an Ocular Plastic Surgeon (www.asoprs.org).
I believe that you can be helped but I also think that you need to have realistic expectations. I think you are being very hard on yourself. You may be best served by also speaking with a counselor to work out your self image issues.

Dear Need
I agree with Dr. Moelleken on a couple of accounts. First your right eye is more prominent and your left eye sits lower in the face than the right eye. However, it addition to these issues, the left upper eyelid rest about 1 mm lower on the globe than the right upper eyelid. This contributes to the left eye looking smaller. Ptosis surgery has the potential to improve this.
However, it is not normal for this type of small difference to be socially crippling. When these feeling exist, it suggest the presence of body dysmorphic disorder. Other signs would be abnormal preoccupation with these differences. An example would be spending hours a day obsessing about this problem. It is my expereince that there is no surgical cure for body dysmorphic disorder(BDD). The BDD brain is organized different than normal brains. This makes it very difficult to surgically help individuals with BDD because once one issue is improved, the brain will focus on how the fix was not every thing that was desired and as a result the person feel social incapacitated by embarrassment.
The best place to start is with psychotherapy to better understand why the brain fixates on these issues. Once you have insight regarding the BDD, it is usually easier to address the issues that benefit from surgery.