Asymmetric eyelids. Left eye appears to bulge out. What can I do?

I think your eyes look fine, what little of them you have shown us.Please be very careful that you do not over educate yourself into trouble.  I see it all the time.  You have such a good idea of what you need that you find someone to do just that even if it is not actually the right thing.Yes there are websites that talk about placing fat pearls in the upper eyelids to create volume.  You would not know from these websites that many, many of these surgeries can create horrible complications.  Think of it this way, the most important job of an upper eyelid is opening and closing.  Each piece of grafted fat forms scars.  With enough scar tissue the eyelid is no longer able to properly open and close.Please be careful out these, a little knowledge can be a dangerous thing.

You need to consult an occuloplastic surgeon.  Part of it could be ptosis and perhaps some proptosis (bulging).  Thyroid function can affect this too.

There are a number or things that can be done to even the eyelids from asymmetric surgery to, as you discovered, fillers or fat. You must also remember that everyone has asymmetry and, sometimes, nothing can be done to correct this. Unfortunately the picture you provided is of such low resolution that I can give no further advice. You need to just see a board certified plastic surgeon who specializes in the eyes or an ophthalmic plastic surgeon who specializes in the external lids.