An oculoplastics consultation would be wise. You may have a normal degree of asymmetry, but even if this is longstanding, it would be good to have a diagnosis. Thyroid problems, sinus problems, refractive differences, and many other etiologies can cause one eye to appear larger than the other....
Simplest thing to do is remove more skin. You are young and should have adequate volume. It is clear that you have a reservoir of skin that would permit safe revision surgery that would not impact your lid closure in a negative way. I wouldn't inject filler in your lids for...
Under eye hollowing can normally be fixed with volume replacement. Fillers that are Hyaluronic Acid based are best for that sensitive area. There are different types of HA fillers and a consultation with a trained injector is best to decide which on is right for you. A good way to find an e...