I have big bulging/protruding eyes, what surgery do I need? I have old and new pictures. (photos)

You have high myopia, so your actual eyeballs have an elongated axial diameter.  This alone could explain the prominence or "bulginess" of the eyes.However, I would also recommend that you have your thyroid labs tested.  Thyroid Eye Disease is a dynamic process that will cause swelling of the eye socket and progressive bulging of the eyes.  If your thyroid labs are normal and your eyes have not been progressively bulging since your eye prescription stabilized, then it is unlikely that the bulging is from thyroid eye disease.To truly reduce the prominence and protrusion of the eyes, the treatment is an orbital decompression.  I would recommend a lateral wall decompression with fat removal, and this would be less likely to cause any double vision.  Some oculoplastic surgeons rarely do this operation and may not have much experience performing it--if you read about it, complications can including meningitis, blindness, or double vision.  However, if you find a high-volume orbital surgeon who does these operations on a routine basis and is well trained, the lateral wall decompression is a safe and effective operation in the right hands.Non-surgically, you could apply fillers to the beneath the lower lids to try to mask the prominence by building up the surrounding tissues around the eyes, but this will not yield a "home-run" type of outcome and would be more of a very mild incremental improvement.

Your principle problem here is upper eyelid ptosis with a profound anterior elevator dehiscence.  Repairing this issue will brighten the eyes and help restore the jewel like quality.  Try to avoid more surgery in your life than you need.

You likely have large myopic eyeballs, which make it look bulging. The bulging appearance is a cosmetic issue, and you may be a candidate for orbital decompression surgery. See link below. This procedure will not change the vision so your high myopia will remain.