One eye protrudes more than the other? Could I have juvederm injected below the larger eye? (Photo)

There are several options, both nonsurgical and surgical, each with pros and cons. See following page. Personal consultation is necessary. Skype okay.

A combination approach will give the most improvement. Fillers, lasers, and microneedling/PRP can improve under the eyes. These fillers (belotero, volbella, restylane silk) are good for this area. I recommend getting a formal evaluation with a cosmetic dermatologist. Best, Dr. Emer

Eyes that protrude forward can be due to something going on behind the eye like autoimmune disease (thyroid is the most common), benign masses or even cancer. Pursue a complete eye evaluation with an Oculofacial Plastic Surgeon. 
A CT scan of the orbits can show the area behind your eye and determine whether the fat is expanded, the muscles are enlarged or other findings. 
Even if all turns out to be fine and this is just a natural asymmetry, I don't think fillers are your best option for improving your appearance. 

I think this needs a full evaluation to determine the exact problem. It appears that one of the upper eyelids is lower than the other which might suggest ptosis. This is usually a surgical problem. However, improving things with fillers is possible as well. Consider an evaluation by an Oculoplastic Surgeon who can lay out all the options for you. Juvederm is the worst filler for the eye area because it can cause prolonged swelling due to it hydrophillic qualities.

Fillers can be used to add volume to the area and disguise irregularities.  I recommend visiting with an experienced injector for an evaluation before beginning.  You want to ensure that the right product is selected and that your goals for treatment are discussed.

The photo you've submitted does not show your concern. The position of the eyes should not change with time, just becomes more obvious in some individuals. I would recommend adding your own fat for better symmetry.Good luck from NYC

the problem seems to be your upper lid and brow area more than the lower lid. This can be remedied with fillers