Eye bag on left side of face. Slight protrusion along tear trough on right side of face. What can I do about this? (photos)

these are very difficult to completely resolve. But I have been able to minimize them with fillers in the area. The injector has to be careful, since the injector can exaggerate the problem even farther. so they need to be experience to how to use the fillers and what type of fillers for this problem. 

 When patients have bags present in the lower eyelids, it is usually the result of fatty deposits creating the puffy look.  Due to facial asymmetry, one eyelid is almost always worse than the other one.  A trans-conjunctival approach can accomplish removal of the herniated fat through an incision on the inside of the eyelid.  Festoons and malar bags will not be improved.  For more information andmany examples, please see the link and the video below

Malay bags are like having swollen legs. They can get worse with fillers because they are areas of swelling.

You appear to have no "eye bags," but, instead, "tear troughs," depressions because of the underlying muscle and ligaments and early relaxation of the tissues. Although a properly done blepharoplasty can correct this, the simplest and safest method is use of a filler. This has to be done by someone very familiar with the anatomy and use of fillers in this area to prevent problems. The only fillers I would use here is Juvederm Voluma, Radiesse or fat. Of these, fat is the most long lasting. Of the other two, Voluma lasts on the average 6 months or more longer than Radiesse (generally 2 years or more). All frequently require a 2nd injection to get the optimal result. Make sure you see someone with significant experience in both off the shelf fillers and fat and treatment of this area. (See ExpertInjector.org and plasticsurgerytoday.com/non-surgical/todays-liquid-lift-wrinkle-and-contour-correction/)