Thank you for your question and your photosI best recommend that you have stem cell enriched fat transfer in order to have a better result as you have volume loss in the supportive fat pads. Removing the excess skin tissue will not solve problem by itself but lead to depression in the lower eyelid area in a later time period. You can not compare your eye with your cousin as you have different eyes and size and she has more volume on her face.
In my opinion this is a surgical problem and it is a mistake to let surgeon filler your upper eyelid with fillers. It is helpful to have a detailed personal consultation to confirm that surgery is right for you. This is a fairly common situation. As the upper eyelid tendon gives away inside the upper eyelid, the anterior orbital fat retracts into the orbit. At the time of surgery, a hard crease is made and the upper eyelid tendon is anchored to this new crease. The anterior orbital fat is mobilize forward. After surgery as the eyelid heals, the eyebrow tend to relax down helping to fill the hollow area. This would bring your appearance closer to that of your cousin. These are not routine surgeries and it is improbable that you will find someone close to home to perform this type of work.
freshmentality, there is nothing wrong with your upper eyelid area but I'm sure someone would be happy to inject something up there to mimic your cousin; I would consider this a mistake. your lower lids would be helped by a "SOOF lift blepharoplasty"; see video and search the Internet for a surgeon near you that is trained in that approach. Good luck!
I think that you don't like the look of your eyes because there is hollowness of the upper eyelid, brow, and lower eyelid. Your cousin's photo is different because she has more fat in her brow (the brow is not just where the eyebrow sits..it is also the thicker skin that extends down toward the eyelids. You might benefit from some filler, like Juvederm or Restylane, to increase the fullness of your brow and possibly the area under your eyes. The trick is to do this is subtle way. In other words, make the area around your eyes a little fuller. If you try and get as much fullness as your cousin you will not get a natural result. The goal should be to look like you, but still have some improvement in the areas you don't like.This is an advanced injection area, so you should see a doctor who is experienced in these type of treatments.
Everyone's eyes look different and beauty comes in different shapes and forms. Subtle improvements are possible. Best to see an oculoplastic specialist. See following link too.
Thank you for sharing your case and photos. Your eyes look perfect. I would not recommend any surgery or procedures to change them. Sometimes, we can be our own worst critic. You may want to schedule a consultation with a board certified oculoplastic surgeon to discuss your concerns further in the office. Good luck!