When I smile, I see these bulges under my eyes. What procedure can make these fat ugly bulges under my eyes go away? (photo)

This can be improved with well-placed botox and/or fillers. Results will last 3-4 months with Botox. I recommend getting a formal evaluation with a cosmetic dermatologist. Best, Dr. Emer

You do not have eye bags. What you have is a normal phenomenon of mild bulging of the muscle around your eyes, the orbicularis oculi, that occurs when smiling. The easiest remedy is a very low dose Botox into the muscle to decrease its activity. In people that have other reasons than this for lower eyelid surgery this muscle can be thinned during the surgery. 
I would advise you to not focus too much on this issue since it is only you that really notices it. Again, this is a normal phenomenon.

What you are seeing is the orbicularis muscle which will pop out when you smile.  Some Botox to the muscle will help keep it flatter. You do not have any prolapsed fat - if anything you are a little hollow.  A little HA filler to the tear trough would help with the skin texture. 

Lower eye bulges can be treated conservatively with Botox or Dysport to help relax the muscle that contributes to the bulge. On the other hand, lower eye bulges can also be from fat (excess or insufficient) in certain areas. If you haven't already, then speak with a plastic surgeon to review possible treatment options with you.Best,Dr. Chaboki

Fillers and laser for under your eyes will give you more volume and will help you with the little hollowness you have there. The laser will tighten your skin and will give you small lift in the eye area, whereas fillers will plump up the extra skin that you claim to have. For both treatments, there is a possibility that you may need more than one treatment to see the best result.

Thanks for your sharing your question and photos.  The bulges you describe is caused from a prominent orbicularis muscle. The judicious use of Botox and/or conservative hyaluronic dermal fillers to the area may soften the bulge.  Best wishes. 

You do not have bags per se.  The fullness you see under the eye is from muscle activity.  You may consider a small dose of botox to relax this muscle.  You can add a conservative amount of filler as well if you choose.  Be sure to see an experienced injector for this delicate area.

Thank you for your question and photo!  The issue you are noticing is called an orbicularis roll. It is caused by bunching on the skin and muscle under your eye when the orbicularis muscle contracts. This can be treated very easily with Botox. Best of luck!