Do people notice my eye asymmetry/best options to fix it? (photo)

It appears you have a large right eye and eye socket but personal consultation is necessary to determine exactly what is the cause of the eye asymmetry which would determine possible treatments.

Thank you for your question and photo.
Yes, I do see the asymmetry that you are noticing; however, what is most important is whether or not it bothers you. If you look closely, many many people have facial asymmetry just like yours. Some people might say that symmetry is beauty, but actually if you look at models and other people that are considered "beautiful," many of them have facial asymmetry just like yours. Take a look at Ryan Gosling for example. His left eye is significantly "smaller" than the right.
While the asymmetries you are noticing can be addressed, my advice is that if it doesn't bother you, enjoy the aspects of your face that make you look like you.
If you do decide that it bothers you, consider finding an oculoplastic surgeon in your area for an in-person consultation and find someone who is on your same "wavelength" about what you are hoping to achieve.
Best of luck!