What's the best procedure to get rid of bulging under eye when smiling? (Photo)

You may benefit from a lower blepharoplasty and the fat can be transposed to fill in the hollow areas that you dislike.

Best Wishes,

Gary Horndeski, M.D.

Under-Eye "Puffy Pillows" is a kind Lymphedema (lymphatic obstruction) that has been related to too superficial injection of an HA filler in the thin, delicate tissues under the eyes and/or the use of an inappropriate choice of HA filler for that region. It tends to be a difficult and persistent problem.
I have had gratifying results in treating this using an algorithm of varying combinations, concentrations and amounts of intralesional anti-inflammatory agents. You would be wise to consult with an experienced, board certified cosmetic dermatologist. Best of luck.

You have a thin layer of fat overlying your orbicularis muscles. For now just monitor them. Treatment is premature. Follow up with an experienced oculoplastic surgeon in a couple of years.
Good luck!