Midface hypoplasia (lack of cheek projection) is common finding which gives the appearance of prominent eyes. Cheek enhancement would most directly address this appearance. Your eyes actually seem to be in a normal position. Filler injection is a good conservative option to give you an idea of what an implant might look like. Be cautious and take your time thinking about your options. Orbital surgery has significant risks and down time - whereas fillers have little or no down time. Best wishes.
Orbital decompression is a potentially complicated operation which can involve removal of orbital bone. It is generally done for eyes that bulge from Thyroid conditions. In reviewing your pictures, you do not appear to have protruding eyes so I do not believe that orbital decompression would make you any happier with your appearance. In addition, the risk of complications of bony orbital decompression surgery are greater than that of a traditional blepharoplasty. The area below your eyelids appear to be shallow and could potentially be improved with dermal fillers or cheek implants. You should seek several qualified opinions with Oculoplastic Surgeons before proceeding.
It is best to obtain personal consultation with an experienced orbital decompression surgery. Orbital decompression can be done for cosmetic purposes, but benefits and risks need to be evaluated. See following link.
The answer to your question is actually quite complex. You should discuss your concerns with a qualified orbital and cosmetic surgeon who has done hundreds if not thousands of decompressions. Many times this surgery is done in an aggressive way but there are new minimally invasive techniques which can alter the eye position very well (often without any skin incisions or bone removal). However, each approach should be customized for each patient.
A number of aggressive surgeons are getting into the orbital decompression as a cosmetic surgery business. Undoubtedly they will be far more willing to perform an orbital decompression for you you. Be careful what you look for as you might find it.
Orbital decompression is almost always performed to protect the eye when it has become pushed forward in the eye socket and is drying out or the optic nerve is being compressed or stretched. It is done occasionally for cosmetic reasons, but given the risks associated, this isn't too common. You need to see a qualified orbital surgeon and discuss all the possible risks before signing up for this kind of surgery. There may be other treatments that will make your eyes appear less prominent, such as cheek enhancement with fillers or implants, which may be less risky and more predictable.
Thank you for posting about your condition. I am glad that your primary doctor has already checked for some of the more common causes of bulging eyes. In many people, this can be a genetic condition. Orbital decompression is a serious surgery with risks. You should schedule a consultation with a board certified oculoplastic surgeon to discuss your goals and see if you are a candidate. Good luck!