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

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.